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

Percentage Accurate: 77.3% → 91.5%

Time: 17.2s

Alternatives: 16

Speedup: 1.0×

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: 77.3% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+123}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{a - t} + \frac{a}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.45e+61)
   (+ x (/ y (/ t (- z a))))
   (if (<= t 6.6e+123)
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (- x (* y (+ (/ z (- a t)) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.45e+61) {
		tmp = x + (y / (t / (z - a)));
	} else if (t <= 6.6e+123) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.45d+61)) then
        tmp = x + (y / (t / (z - a)))
    else if (t <= 6.6d+123) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = x - (y * ((z / (a - t)) + (a / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.45e+61) {
		tmp = x + (y / (t / (z - a)));
	} else if (t <= 6.6e+123) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.45e+61:
		tmp = x + (y / (t / (z - a)))
	elif t <= 6.6e+123:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x - (y * ((z / (a - t)) + (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.45e+61)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	elseif (t <= 6.6e+123)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z / Float64(a - t)) + Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.45e+61)
		tmp = x + (y / (t / (z - a)));
	elseif (t <= 6.6e+123)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.45e+61], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+123], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.45000000000000013e61

   1. Initial program 55.2%

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

      1. associate--l+ 57.5%

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

      2. sub-neg 57.5%

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

      3. distribute-frac-neg 57.5%

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

      4. distribute-rgt-neg-out 57.5%

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

      5. +-commutative 57.5%

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

      6. distribute-rgt-neg-out 57.5%

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

      7. distribute-lft-neg-in 57.5%

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

      8. associate-/l* 73.4%

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

      9. associate-/r/ 77.8%

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

      10. fma-def 77.8%

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

      11. sub-neg 77.8%

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

      12. distribute-neg-in 77.8%

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

      13. remove-double-neg 77.8%

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

      14. +-commutative 77.8%

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

      15. sub-neg 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in t around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. neg-mul-1 62.6%

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

      3. associate-+r+ 80.4%

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

      4. neg-mul-1 80.4%

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

      5. distribute-rgt1-in 80.4%

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

      6. metadata-eval 80.4%

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

      7. mul0-lft 80.4%

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

      8. associate-/l* 91.2%

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

   6. Simplified 91.2%

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

   if -2.45000000000000013e61 < t < 6.60000000000000006e123

   1. Initial program 89.2%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   if 6.60000000000000006e123 < t

   1. Initial program 57.8%

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

      1. associate--l+ 61.8%

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

      2. sub-neg 61.8%

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

      3. distribute-frac-neg 61.8%

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

      4. distribute-rgt-neg-out 61.8%

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

      5. +-commutative 61.8%

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

      6. distribute-rgt-neg-out 61.8%

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

      7. distribute-lft-neg-in 61.8%

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

      8. associate-/l* 69.2%

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

      9. associate-/r/ 80.9%

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

      10. fma-def 80.8%

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

      11. sub-neg 80.8%

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

      12. distribute-neg-in 80.8%

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

      13. remove-double-neg 80.8%

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

      14. +-commutative 80.8%

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

      15. sub-neg 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in y around 0 88.6%

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

   5. Taylor expanded in t around inf 92.8%

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

      1. associate-*r/ 92.8%

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

      2. mul-1-neg 92.8%

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

   7. Simplified 92.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+123}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{a - t} + \frac{a}{t}\right)\\ \end{array} \]

Alternative 2: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+20}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-30}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e+76)
   (+ x y)
   (if (<= a -7e+20)
     (- x (/ y (/ a z)))
     (if (<= a 1.35e-136)
       (+ x (/ (* y z) t))
       (if (<= a 4e-30)
         (- x (/ a (/ t y)))
         (if (<= a 2.8e+57) (+ x (* y (/ z t))) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+76) {
		tmp = x + y;
	} else if (a <= -7e+20) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.35e-136) {
		tmp = x + ((y * z) / t);
	} else if (a <= 4e-30) {
		tmp = x - (a / (t / y));
	} else if (a <= 2.8e+57) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d+76)) then
        tmp = x + y
    else if (a <= (-7d+20)) then
        tmp = x - (y / (a / z))
    else if (a <= 1.35d-136) then
        tmp = x + ((y * z) / t)
    else if (a <= 4d-30) then
        tmp = x - (a / (t / y))
    else if (a <= 2.8d+57) then
        tmp = x + (y * (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+76) {
		tmp = x + y;
	} else if (a <= -7e+20) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.35e-136) {
		tmp = x + ((y * z) / t);
	} else if (a <= 4e-30) {
		tmp = x - (a / (t / y));
	} else if (a <= 2.8e+57) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e+76:
		tmp = x + y
	elif a <= -7e+20:
		tmp = x - (y / (a / z))
	elif a <= 1.35e-136:
		tmp = x + ((y * z) / t)
	elif a <= 4e-30:
		tmp = x - (a / (t / y))
	elif a <= 2.8e+57:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e+76)
		tmp = Float64(x + y);
	elseif (a <= -7e+20)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (a <= 1.35e-136)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 4e-30)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (a <= 2.8e+57)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e+76)
		tmp = x + y;
	elseif (a <= -7e+20)
		tmp = x - (y / (a / z));
	elseif (a <= 1.35e-136)
		tmp = x + ((y * z) / t);
	elseif (a <= 4e-30)
		tmp = x - (a / (t / y));
	elseif (a <= 2.8e+57)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e+76], N[(x + y), $MachinePrecision], If[LessEqual[a, -7e+20], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-136], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-30], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+57], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.4999999999999999e76 or 2.8e57 < a

   1. Initial program 81.7%

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

      1. associate--l+ 81.7%

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

      2. sub-neg 81.7%

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

      3. distribute-frac-neg 81.7%

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

      4. distribute-rgt-neg-out 81.7%

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

      5. +-commutative 81.7%

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

      6. distribute-rgt-neg-out 81.7%

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

      7. distribute-lft-neg-in 81.7%

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

      8. associate-/l* 90.9%

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

      9. associate-/r/ 92.3%

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

      10. fma-def 92.3%

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

      11. sub-neg 92.3%

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

      12. distribute-neg-in 92.3%

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

      13. remove-double-neg 92.3%

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

      14. +-commutative 92.3%

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

      15. sub-neg 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in a around inf 84.7%

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

      1. +-commutative 84.7%

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

   6. Simplified 84.7%

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

   if -1.4999999999999999e76 < a < -7e20

   1. Initial program 63.2%

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

      1. associate--l+ 73.1%

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

      2. sub-neg 73.1%

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

      3. distribute-frac-neg 73.1%

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

      4. distribute-rgt-neg-out 73.1%

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

      5. +-commutative 73.1%

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

      6. distribute-rgt-neg-out 73.1%

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

      7. distribute-lft-neg-in 73.1%

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

      8. associate-/l* 87.7%

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

      9. associate-/r/ 90.7%

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

      10. fma-def 90.7%

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

      11. sub-neg 90.7%

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

      12. distribute-neg-in 90.7%

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

      13. remove-double-neg 90.7%

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

      14. +-commutative 90.7%

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

      15. sub-neg 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around inf 73.5%

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

      1. mul-1-neg 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in a around inf 70.4%

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

      1. mul-1-neg 70.4%

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

      2. sub-neg 70.4%

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

      3. associate-/l* 80.5%

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

   9. Simplified 80.5%

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

   if -7e20 < a < 1.3499999999999999e-136

   1. Initial program 76.2%

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

      1. associate--l+ 80.5%

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

      2. sub-neg 80.5%

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

      3. distribute-frac-neg 80.5%

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

      4. distribute-rgt-neg-out 80.5%

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

      5. +-commutative 80.5%

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

      6. distribute-rgt-neg-out 80.5%

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

      7. distribute-lft-neg-in 80.5%

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

      8. associate-/l* 84.6%

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

      9. associate-/r/ 85.5%

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

      10. fma-def 85.5%

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

      11. sub-neg 85.5%

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

      12. distribute-neg-in 85.5%

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

      13. remove-double-neg 85.5%

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

      14. +-commutative 85.5%

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

      15. sub-neg 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in y around 0 92.4%

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

   5. Taylor expanded in a around 0 81.0%

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

   if 1.3499999999999999e-136 < a < 4e-30

   1. Initial program 85.8%

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

      1. associate--l+ 88.6%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around inf 65.3%

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

      1. distribute-lft-out-- 65.3%

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

      2. associate-*r/ 65.3%

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

      3. mul-1-neg 65.3%

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

      4. *-commutative 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in z around 0 69.0%

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

      1. associate-/l* 71.8%

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

   9. Simplified 71.8%

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

   if 4e-30 < a < 2.8e57

   1. Initial program 81.3%

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

      1. associate--l+ 81.8%

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

      2. sub-neg 81.8%

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

      3. distribute-frac-neg 81.8%

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

      4. distribute-rgt-neg-out 81.8%

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

      5. +-commutative 81.8%

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

      6. distribute-rgt-neg-out 81.8%

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

      7. distribute-lft-neg-in 81.8%

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

      8. associate-/l* 82.7%

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

      9. associate-/r/ 90.7%

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

      10. fma-def 90.7%

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

      11. sub-neg 90.7%

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

      12. distribute-neg-in 90.7%

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

      13. remove-double-neg 90.7%

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

      14. +-commutative 90.7%

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

      15. sub-neg 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in y around 0 95.1%

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

   5. Taylor expanded in a around 0 77.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+20}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-30}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+20}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-139}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.42e+82)
   (+ x y)
   (if (<= a -5e+20)
     (- x (/ y (/ a z)))
     (if (<= a 1.5e-139)
       (+ x (/ (* y z) t))
       (if (<= a 1.2e-25)
         (- x (/ (* y z) a))
         (if (<= a 6e+57) (+ x (* y (/ z t))) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.42e+82) {
		tmp = x + y;
	} else if (a <= -5e+20) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.5e-139) {
		tmp = x + ((y * z) / t);
	} else if (a <= 1.2e-25) {
		tmp = x - ((y * z) / a);
	} else if (a <= 6e+57) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.42d+82)) then
        tmp = x + y
    else if (a <= (-5d+20)) then
        tmp = x - (y / (a / z))
    else if (a <= 1.5d-139) then
        tmp = x + ((y * z) / t)
    else if (a <= 1.2d-25) then
        tmp = x - ((y * z) / a)
    else if (a <= 6d+57) then
        tmp = x + (y * (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.42e+82) {
		tmp = x + y;
	} else if (a <= -5e+20) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.5e-139) {
		tmp = x + ((y * z) / t);
	} else if (a <= 1.2e-25) {
		tmp = x - ((y * z) / a);
	} else if (a <= 6e+57) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.42e+82:
		tmp = x + y
	elif a <= -5e+20:
		tmp = x - (y / (a / z))
	elif a <= 1.5e-139:
		tmp = x + ((y * z) / t)
	elif a <= 1.2e-25:
		tmp = x - ((y * z) / a)
	elif a <= 6e+57:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.42e+82)
		tmp = Float64(x + y);
	elseif (a <= -5e+20)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (a <= 1.5e-139)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 1.2e-25)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	elseif (a <= 6e+57)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.42e+82)
		tmp = x + y;
	elseif (a <= -5e+20)
		tmp = x - (y / (a / z));
	elseif (a <= 1.5e-139)
		tmp = x + ((y * z) / t);
	elseif (a <= 1.2e-25)
		tmp = x - ((y * z) / a);
	elseif (a <= 6e+57)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.42e+82], N[(x + y), $MachinePrecision], If[LessEqual[a, -5e+20], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-139], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-25], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+57], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.41999999999999993e82 or 5.9999999999999999e57 < a

   1. Initial program 81.7%

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

      1. associate--l+ 81.7%

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

      2. sub-neg 81.7%

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

      3. distribute-frac-neg 81.7%

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

      4. distribute-rgt-neg-out 81.7%

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

      5. +-commutative 81.7%

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

      6. distribute-rgt-neg-out 81.7%

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

      7. distribute-lft-neg-in 81.7%

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

      8. associate-/l* 90.9%

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

      9. associate-/r/ 92.3%

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

      10. fma-def 92.3%

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

      11. sub-neg 92.3%

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

      12. distribute-neg-in 92.3%

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

      13. remove-double-neg 92.3%

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

      14. +-commutative 92.3%

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

      15. sub-neg 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in a around inf 84.7%

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

      1. +-commutative 84.7%

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

   6. Simplified 84.7%

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

   if -1.41999999999999993e82 < a < -5e20

   1. Initial program 63.2%

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

      1. associate--l+ 73.1%

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

      2. sub-neg 73.1%

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

      3. distribute-frac-neg 73.1%

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

      4. distribute-rgt-neg-out 73.1%

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

      5. +-commutative 73.1%

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

      6. distribute-rgt-neg-out 73.1%

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

      7. distribute-lft-neg-in 73.1%

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

      8. associate-/l* 87.7%

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

      9. associate-/r/ 90.7%

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

      10. fma-def 90.7%

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

      11. sub-neg 90.7%

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

      12. distribute-neg-in 90.7%

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

      13. remove-double-neg 90.7%

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

      14. +-commutative 90.7%

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

      15. sub-neg 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around inf 73.5%

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

      1. mul-1-neg 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in a around inf 70.4%

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

      1. mul-1-neg 70.4%

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

      2. sub-neg 70.4%

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

      3. associate-/l* 80.5%

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

   9. Simplified 80.5%

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

   if -5e20 < a < 1.5e-139

   1. Initial program 75.9%

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

      1. associate--l+ 80.3%

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

      2. sub-neg 80.3%

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

      3. distribute-frac-neg 80.3%

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

      4. distribute-rgt-neg-out 80.3%

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

      5. +-commutative 80.3%

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

      6. distribute-rgt-neg-out 80.3%

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

      7. distribute-lft-neg-in 80.3%

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

      8. associate-/l* 84.5%

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

      9. associate-/r/ 85.4%

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

      10. fma-def 85.3%

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

      11. sub-neg 85.3%

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

      12. distribute-neg-in 85.3%

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

      13. remove-double-neg 85.3%

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

      14. +-commutative 85.3%

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

      15. sub-neg 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around 0 92.3%

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

   5. Taylor expanded in a around 0 80.8%

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

   if 1.5e-139 < a < 1.20000000000000005e-25

   1. Initial program 86.6%

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

      1. associate--l+ 89.3%

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

      2. sub-neg 89.3%

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

      3. distribute-frac-neg 89.3%

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

      4. distribute-rgt-neg-out 89.3%

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

      5. +-commutative 89.3%

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

      6. distribute-rgt-neg-out 89.3%

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

      7. distribute-lft-neg-in 89.3%

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

      8. associate-/l* 91.9%

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

      9. associate-/r/ 89.2%

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

      10. fma-def 89.3%

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

      11. sub-neg 89.3%

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

      12. distribute-neg-in 89.3%

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

      13. remove-double-neg 89.3%

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

      14. +-commutative 89.3%

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

      15. sub-neg 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 91.3%

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

      1. mul-1-neg 91.3%

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

   6. Simplified 91.3%

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

   7. Taylor expanded in t around 0 75.0%

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

   if 1.20000000000000005e-25 < a < 5.9999999999999999e57

   1. Initial program 80.4%

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

      1. associate--l+ 80.9%

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

      2. sub-neg 80.9%

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

      3. distribute-frac-neg 80.9%

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

      4. distribute-rgt-neg-out 80.9%

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

      5. +-commutative 80.9%

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

      6. distribute-rgt-neg-out 80.9%

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

      7. distribute-lft-neg-in 80.9%

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

      8. associate-/l* 81.8%

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

      9. associate-/r/ 90.3%

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

      10. fma-def 90.2%

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

      11. sub-neg 90.2%

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

      12. distribute-neg-in 90.2%

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

      13. remove-double-neg 90.2%

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

      14. +-commutative 90.2%

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

      15. sub-neg 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around 0 94.9%

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

   5. Taylor expanded in a around 0 80.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+20}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-139}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 91.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+61} \lor \neg \left(t \leq 9.5 \cdot 10^{+127}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.4e+61) (not (<= t 9.5e+127)))
   (+ x (/ y (/ t (- z a))))
   (+ x (+ y (/ (- t z) (/ (- a t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.4e+61) || !(t <= 9.5e+127)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.4d+61)) .or. (.not. (t <= 9.5d+127))) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.4e+61) || !(t <= 9.5e+127)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.4e+61) or not (t <= 9.5e+127):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.4e+61) || !(t <= 9.5e+127))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.4e+61) || ~((t <= 9.5e+127)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.4e+61], N[Not[LessEqual[t, 9.5e+127]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.40000000000000005e61 or 9.49999999999999975e127 < t

   1. Initial program 56.4%

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

      1. associate--l+ 59.5%

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

      2. sub-neg 59.5%

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

      3. distribute-frac-neg 59.5%

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

      4. distribute-rgt-neg-out 59.5%

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

      5. +-commutative 59.5%

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

      6. distribute-rgt-neg-out 59.5%

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

      7. distribute-lft-neg-in 59.5%

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

      8. associate-/l* 71.5%

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

      9. associate-/r/ 79.2%

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

      10. fma-def 79.2%

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

      11. sub-neg 79.2%

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

      12. distribute-neg-in 79.2%

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

      13. remove-double-neg 79.2%

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

      14. +-commutative 79.2%

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

      15. sub-neg 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in t around inf 64.9%

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

      1. +-commutative 64.9%

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

      2. neg-mul-1 64.9%

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

      3. associate-+r+ 79.8%

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

      4. neg-mul-1 79.8%

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

      5. distribute-rgt1-in 79.8%

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

      6. metadata-eval 79.8%

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

      7. mul0-lft 79.8%

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

      8. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

   if -7.40000000000000005e61 < t < 9.49999999999999975e127

   1. Initial program 89.2%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+61} \lor \neg \left(t \leq 9.5 \cdot 10^{+127}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \]

Alternative 5: 93.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (- (+ (/ t (- a t)) 1.0) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (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 * (((t / (a - t)) + 1.0d0) - (z / (a - t))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))));
}

Python

def code(x, y, z, t, a):
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(Float64(t / Float64(a - t)) + 1.0) - Float64(z / Float64(a - t)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.9%

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

   1. associate--l+ 81.6%

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

   2. sub-neg 81.6%

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

   3. distribute-frac-neg 81.6%

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

   4. distribute-rgt-neg-out 81.6%

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

   5. +-commutative 81.6%

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

   6. distribute-rgt-neg-out 81.6%

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

   7. distribute-lft-neg-in 81.6%

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

   8. associate-/l* 87.7%

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

   9. associate-/r/ 89.0%

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

   10. fma-def 88.9%

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

   11. sub-neg 88.9%

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

   12. distribute-neg-in 88.9%

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

   13. remove-double-neg 88.9%

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

   14. +-commutative 88.9%

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

   15. sub-neg 88.9%

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

3. Simplified 88.9%

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

4. Taylor expanded in y around 0 92.4%

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

5. Final simplification 92.4%

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

Alternative 6: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-72}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e-72)
   (+ x y)
   (if (<= a 1.35e-136)
     (+ x (/ (* y z) t))
     (if (<= a 3.2e-30)
       (- x (/ a (/ t y)))
       (if (<= a 5.9e+57) (+ x (* y (/ z t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e-72) {
		tmp = x + y;
	} else if (a <= 1.35e-136) {
		tmp = x + ((y * z) / t);
	} else if (a <= 3.2e-30) {
		tmp = x - (a / (t / y));
	} else if (a <= 5.9e+57) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.1d-72)) then
        tmp = x + y
    else if (a <= 1.35d-136) then
        tmp = x + ((y * z) / t)
    else if (a <= 3.2d-30) then
        tmp = x - (a / (t / y))
    else if (a <= 5.9d+57) then
        tmp = x + (y * (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e-72) {
		tmp = x + y;
	} else if (a <= 1.35e-136) {
		tmp = x + ((y * z) / t);
	} else if (a <= 3.2e-30) {
		tmp = x - (a / (t / y));
	} else if (a <= 5.9e+57) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e-72:
		tmp = x + y
	elif a <= 1.35e-136:
		tmp = x + ((y * z) / t)
	elif a <= 3.2e-30:
		tmp = x - (a / (t / y))
	elif a <= 5.9e+57:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e-72)
		tmp = Float64(x + y);
	elseif (a <= 1.35e-136)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 3.2e-30)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (a <= 5.9e+57)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e-72)
		tmp = x + y;
	elseif (a <= 1.35e-136)
		tmp = x + ((y * z) / t);
	elseif (a <= 3.2e-30)
		tmp = x - (a / (t / y));
	elseif (a <= 5.9e+57)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e-72], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.35e-136], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-30], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.9e+57], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.1e-72 or 5.90000000000000013e57 < a

   1. Initial program 77.3%

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

      1. associate--l+ 78.7%

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

      2. sub-neg 78.7%

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

      3. distribute-frac-neg 78.7%

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

      4. distribute-rgt-neg-out 78.7%

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

      5. +-commutative 78.7%

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

      6. distribute-rgt-neg-out 78.7%

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

      7. distribute-lft-neg-in 78.7%

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

      8. associate-/l* 89.2%

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

      9. associate-/r/ 90.6%

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

      10. fma-def 90.6%

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

      11. sub-neg 90.6%

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

      12. distribute-neg-in 90.6%

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

      13. remove-double-neg 90.6%

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

      14. +-commutative 90.6%

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

      15. sub-neg 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 74.2%

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

      1. +-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -2.1e-72 < a < 1.3499999999999999e-136

   1. Initial program 77.7%

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

      1. associate--l+ 82.8%

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

      2. sub-neg 82.8%

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

      3. distribute-frac-neg 82.8%

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

      4. distribute-rgt-neg-out 82.8%

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

      5. +-commutative 82.8%

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

      6. distribute-rgt-neg-out 82.8%

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

      7. distribute-lft-neg-in 82.8%

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

      8. associate-/l* 85.3%

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

      9. associate-/r/ 86.4%

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

      10. fma-def 86.3%

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

      11. sub-neg 86.3%

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

      12. distribute-neg-in 86.3%

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

      13. remove-double-neg 86.3%

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

      14. +-commutative 86.3%

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

      15. sub-neg 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around 0 93.4%

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

   5. Taylor expanded in a around 0 87.8%

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

   if 1.3499999999999999e-136 < a < 3.2e-30

   1. Initial program 85.8%

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

      1. associate--l+ 88.6%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around inf 65.3%

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

      1. distribute-lft-out-- 65.3%

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

      2. associate-*r/ 65.3%

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

      3. mul-1-neg 65.3%

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

      4. *-commutative 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in z around 0 69.0%

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

      1. associate-/l* 71.8%

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

   9. Simplified 71.8%

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

   if 3.2e-30 < a < 5.90000000000000013e57

   1. Initial program 81.3%

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

      1. associate--l+ 81.8%

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

      2. sub-neg 81.8%

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

      3. distribute-frac-neg 81.8%

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

      4. distribute-rgt-neg-out 81.8%

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

      5. +-commutative 81.8%

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

      6. distribute-rgt-neg-out 81.8%

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

      7. distribute-lft-neg-in 81.8%

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

      8. associate-/l* 82.7%

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

      9. associate-/r/ 90.7%

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

      10. fma-def 90.7%

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

      11. sub-neg 90.7%

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

      12. distribute-neg-in 90.7%

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

      13. remove-double-neg 90.7%

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

      14. +-commutative 90.7%

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

      15. sub-neg 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in y around 0 95.1%

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

   5. Taylor expanded in a around 0 77.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-72}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 86.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+88}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{-y}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e+88)
   (+ x y)
   (if (<= a 6.3e+58)
     (+ x (/ z (/ (- a t) (- y))))
     (+ y (- x (/ y (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e+88) {
		tmp = x + y;
	} else if (a <= 6.3e+58) {
		tmp = x + (z / ((a - t) / -y));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.95d+88)) then
        tmp = x + y
    else if (a <= 6.3d+58) then
        tmp = x + (z / ((a - t) / -y))
    else
        tmp = y + (x - (y / (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e+88) {
		tmp = x + y;
	} else if (a <= 6.3e+58) {
		tmp = x + (z / ((a - t) / -y));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.95e+88:
		tmp = x + y
	elif a <= 6.3e+58:
		tmp = x + (z / ((a - t) / -y))
	else:
		tmp = y + (x - (y / (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e+88)
		tmp = Float64(x + y);
	elseif (a <= 6.3e+58)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / Float64(-y))));
	else
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.95e+88)
		tmp = x + y;
	elseif (a <= 6.3e+58)
		tmp = x + (z / ((a - t) / -y));
	else
		tmp = y + (x - (y / (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e+88], N[(x + y), $MachinePrecision], If[LessEqual[a, 6.3e+58], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9500000000000001e88

   1. Initial program 76.2%

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

      1. associate--l+ 76.1%

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

      2. sub-neg 76.1%

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

      3. distribute-frac-neg 76.1%

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

      4. distribute-rgt-neg-out 76.1%

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

      5. +-commutative 76.1%

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

      6. distribute-rgt-neg-out 76.1%

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

      7. distribute-lft-neg-in 76.1%

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

      8. associate-/l* 89.7%

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

      9. associate-/r/ 89.4%

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

      10. fma-def 89.4%

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

      11. sub-neg 89.4%

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

      12. distribute-neg-in 89.4%

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

      13. remove-double-neg 89.4%

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

      14. +-commutative 89.4%

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

      15. sub-neg 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in a around inf 86.7%

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

      1. +-commutative 86.7%

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

   6. Simplified 86.7%

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

   if -1.9500000000000001e88 < a < 6.2999999999999995e58

   1. Initial program 77.5%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. distribute-frac-neg 81.6%

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

      4. distribute-rgt-neg-out 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-rgt-neg-out 81.6%

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

      7. distribute-lft-neg-in 81.6%

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

      8. associate-/l* 86.0%

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

      9. associate-/r/ 87.3%

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

      10. fma-def 87.2%

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

      11. sub-neg 87.2%

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

      12. distribute-neg-in 87.2%

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

      13. remove-double-neg 87.2%

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

      14. +-commutative 87.2%

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

      15. sub-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in y around 0 91.9%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. associate-*r/ 86.2%

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

      2. associate-*r* 86.2%

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

      3. neg-mul-1 86.2%

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

      4. *-commutative 86.2%

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

      5. associate-/l* 88.1%

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

   7. Simplified 88.1%

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

   if 6.2999999999999995e58 < a

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate--l+ 84.5%

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

      3. sub-neg 84.5%

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

      4. distribute-frac-neg 84.5%

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

      5. distribute-rgt-neg-out 84.5%

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

      6. distribute-rgt-neg-out 84.5%

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

      7. distribute-frac-neg 84.5%

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

      8. sub-neg 84.5%

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

      9. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 84.6%

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

      1. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+88}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{-y}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \]

Alternative 8: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+47} \lor \neg \left(t \leq 1.45 \cdot 10^{-61}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+47) (not (<= t 1.45e-61)))
   (+ x (* y (/ z t)))
   (+ y (- x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+47) || !(t <= 1.45e-61)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.5d+47)) .or. (.not. (t <= 1.45d-61))) then
        tmp = x + (y * (z / t))
    else
        tmp = y + (x - (y / (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+47) || !(t <= 1.45e-61)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e+47) or not (t <= 1.45e-61):
		tmp = x + (y * (z / t))
	else:
		tmp = y + (x - (y / (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+47) || !(t <= 1.45e-61))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e+47) || ~((t <= 1.45e-61)))
		tmp = x + (y * (z / t));
	else
		tmp = y + (x - (y / (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+47], N[Not[LessEqual[t, 1.45e-61]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.50000000000000011e47 or 1.45e-61 < t

   1. Initial program 66.2%

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

      1. associate--l+ 70.8%

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

      2. sub-neg 70.8%

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

      3. distribute-frac-neg 70.8%

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

      4. distribute-rgt-neg-out 70.8%

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

      5. +-commutative 70.8%

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

      6. distribute-rgt-neg-out 70.8%

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

      7. distribute-lft-neg-in 70.8%

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

      8. associate-/l* 79.7%

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

      9. associate-/r/ 84.4%

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

      10. fma-def 84.4%

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

      11. sub-neg 84.4%

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

      12. distribute-neg-in 84.4%

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

      13. remove-double-neg 84.4%

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

      14. +-commutative 84.4%

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

      15. sub-neg 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in y around 0 89.8%

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

   5. Taylor expanded in a around 0 80.8%

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

   if -2.50000000000000011e47 < t < 1.45e-61

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate--l+ 92.0%

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

      3. sub-neg 92.0%

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

      4. distribute-frac-neg 92.0%

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

      5. distribute-rgt-neg-out 92.0%

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

      6. distribute-rgt-neg-out 92.0%

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

      7. distribute-frac-neg 92.0%

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

      8. sub-neg 92.0%

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

      9. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in t around 0 82.8%

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

      1. associate-/l* 83.3%

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

   6. Simplified 83.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+47} \lor \neg \left(t \leq 1.45 \cdot 10^{-61}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \]

Alternative 9: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+59}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.3e+90)
   (+ x y)
   (if (<= a 1.08e+59) (- x (* y (/ z (- a t)))) (+ y (- x (/ y (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.3e+90) {
		tmp = x + y;
	} else if (a <= 1.08e+59) {
		tmp = x - (y * (z / (a - t)));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.3d+90)) then
        tmp = x + y
    else if (a <= 1.08d+59) then
        tmp = x - (y * (z / (a - t)))
    else
        tmp = y + (x - (y / (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.3e+90) {
		tmp = x + y;
	} else if (a <= 1.08e+59) {
		tmp = x - (y * (z / (a - t)));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.3e+90:
		tmp = x + y
	elif a <= 1.08e+59:
		tmp = x - (y * (z / (a - t)))
	else:
		tmp = y + (x - (y / (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.3e+90)
		tmp = Float64(x + y);
	elseif (a <= 1.08e+59)
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.3e+90)
		tmp = x + y;
	elseif (a <= 1.08e+59)
		tmp = x - (y * (z / (a - t)));
	else
		tmp = y + (x - (y / (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.3e+90], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.08e+59], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.30000000000000008e90

   1. Initial program 76.2%

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

      1. associate--l+ 76.1%

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

      2. sub-neg 76.1%

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

      3. distribute-frac-neg 76.1%

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

      4. distribute-rgt-neg-out 76.1%

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

      5. +-commutative 76.1%

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

      6. distribute-rgt-neg-out 76.1%

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

      7. distribute-lft-neg-in 76.1%

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

      8. associate-/l* 89.7%

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

      9. associate-/r/ 89.4%

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

      10. fma-def 89.4%

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

      11. sub-neg 89.4%

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

      12. distribute-neg-in 89.4%

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

      13. remove-double-neg 89.4%

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

      14. +-commutative 89.4%

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

      15. sub-neg 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in a around inf 86.7%

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

      1. +-commutative 86.7%

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

   6. Simplified 86.7%

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

   if -3.30000000000000008e90 < a < 1.08e59

   1. Initial program 77.5%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. distribute-frac-neg 81.6%

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

      4. distribute-rgt-neg-out 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-rgt-neg-out 81.6%

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

      7. distribute-lft-neg-in 81.6%

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

      8. associate-/l* 86.0%

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

      9. associate-/r/ 87.3%

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

      10. fma-def 87.2%

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

      11. sub-neg 87.2%

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

      12. distribute-neg-in 87.2%

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

      13. remove-double-neg 87.2%

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

      14. +-commutative 87.2%

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

      15. sub-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. mul-1-neg 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in x around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. sub-neg 86.2%

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

      3. *-rgt-identity 86.2%

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

      4. associate-*r/ 86.2%

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

      5. associate-*l* 87.3%

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

      6. *-commutative 87.3%

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

      7. associate-*l/ 87.3%

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

      8. *-lft-identity 87.3%

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

   9. Simplified 87.3%

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

   if 1.08e59 < a

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate--l+ 84.5%

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

      3. sub-neg 84.5%

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

      4. distribute-frac-neg 84.5%

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

      5. distribute-rgt-neg-out 84.5%

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

      6. distribute-rgt-neg-out 84.5%

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

      7. distribute-frac-neg 84.5%

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

      8. sub-neg 84.5%

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

      9. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 84.6%

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

      1. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+59}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \]

Alternative 10: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+88}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+59}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+88)
   (+ x y)
   (if (<= a 3.1e+59) (- x (/ y (/ (- a t) z))) (+ y (- x (/ y (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+88) {
		tmp = x + y;
	} else if (a <= 3.1e+59) {
		tmp = x - (y / ((a - t) / z));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.5d+88)) then
        tmp = x + y
    else if (a <= 3.1d+59) then
        tmp = x - (y / ((a - t) / z))
    else
        tmp = y + (x - (y / (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+88) {
		tmp = x + y;
	} else if (a <= 3.1e+59) {
		tmp = x - (y / ((a - t) / z));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+88:
		tmp = x + y
	elif a <= 3.1e+59:
		tmp = x - (y / ((a - t) / z))
	else:
		tmp = y + (x - (y / (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+88)
		tmp = Float64(x + y);
	elseif (a <= 3.1e+59)
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+88)
		tmp = x + y;
	elseif (a <= 3.1e+59)
		tmp = x - (y / ((a - t) / z));
	else
		tmp = y + (x - (y / (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+88], N[(x + y), $MachinePrecision], If[LessEqual[a, 3.1e+59], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5e88

   1. Initial program 76.2%

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

      1. associate--l+ 76.1%

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

      2. sub-neg 76.1%

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

      3. distribute-frac-neg 76.1%

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

      4. distribute-rgt-neg-out 76.1%

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

      5. +-commutative 76.1%

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

      6. distribute-rgt-neg-out 76.1%

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

      7. distribute-lft-neg-in 76.1%

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

      8. associate-/l* 89.7%

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

      9. associate-/r/ 89.4%

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

      10. fma-def 89.4%

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

      11. sub-neg 89.4%

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

      12. distribute-neg-in 89.4%

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

      13. remove-double-neg 89.4%

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

      14. +-commutative 89.4%

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

      15. sub-neg 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in a around inf 86.7%

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

      1. +-commutative 86.7%

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

   6. Simplified 86.7%

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

   if -4.5e88 < a < 3.10000000000000015e59

   1. Initial program 77.5%

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

      1. associate--l+ 81.6%

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

      2. sub-neg 81.6%

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

      3. distribute-frac-neg 81.6%

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

      4. distribute-rgt-neg-out 81.6%

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

      5. +-commutative 81.6%

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

      6. distribute-rgt-neg-out 81.6%

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

      7. distribute-lft-neg-in 81.6%

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

      8. associate-/l* 86.0%

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

      9. associate-/r/ 87.3%

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

      10. fma-def 87.2%

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

      11. sub-neg 87.2%

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

      12. distribute-neg-in 87.2%

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

      13. remove-double-neg 87.2%

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

      14. +-commutative 87.2%

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

      15. sub-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. mul-1-neg 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in x around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. sub-neg 86.2%

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

      3. associate-/l* 87.3%

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

   9. Simplified 87.3%

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

   if 3.10000000000000015e59 < a

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate--l+ 84.5%

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

      3. sub-neg 84.5%

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

      4. distribute-frac-neg 84.5%

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

      5. distribute-rgt-neg-out 84.5%

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

      6. distribute-rgt-neg-out 84.5%

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

      7. distribute-frac-neg 84.5%

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

      8. sub-neg 84.5%

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

      9. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 84.6%

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

      1. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+88}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+59}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \]

Alternative 11: 76.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+29} \lor \neg \left(a \leq 3 \cdot 10^{+57}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.2e+29) (not (<= a 3e+57))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.2e+29) || !(a <= 3e+57)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.2d+29)) .or. (.not. (a <= 3d+57))) then
        tmp = x + y
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.2e+29) || !(a <= 3e+57)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.2e+29) or not (a <= 3e+57):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.2e+29) || !(a <= 3e+57))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.2e+29) || ~((a <= 3e+57)))
		tmp = x + y;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.2e+29], N[Not[LessEqual[a, 3e+57]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.2e29 or 3e57 < a

   1. Initial program 80.3%

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

      1. associate--l+ 80.8%

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

      2. sub-neg 80.8%

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

      3. distribute-frac-neg 80.8%

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

      4. distribute-rgt-neg-out 80.8%

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

      5. +-commutative 80.8%

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

      6. distribute-rgt-neg-out 80.8%

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

      7. distribute-lft-neg-in 80.8%

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

      8. associate-/l* 90.2%

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

      9. associate-/r/ 91.9%

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

      10. fma-def 91.9%

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

      11. sub-neg 91.9%

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

      12. distribute-neg-in 91.9%

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

      13. remove-double-neg 91.9%

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

      14. +-commutative 91.9%

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

      15. sub-neg 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in a around inf 78.7%

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

      1. +-commutative 78.7%

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

   6. Simplified 78.7%

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

   if -5.2e29 < a < 3e57

   1. Initial program 78.1%

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

      1. associate--l+ 82.1%

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

      2. sub-neg 82.1%

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

      3. distribute-frac-neg 82.1%

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

      4. distribute-rgt-neg-out 82.1%

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

      5. +-commutative 82.1%

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

      6. distribute-rgt-neg-out 82.1%

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

      7. distribute-lft-neg-in 82.1%

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

      8. associate-/l* 86.0%

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

      9. associate-/r/ 87.1%

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

      10. fma-def 87.1%

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

      11. sub-neg 87.1%

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

      12. distribute-neg-in 87.1%

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

      13. remove-double-neg 87.1%

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

      14. +-commutative 87.1%

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

      15. sub-neg 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in y around 0 92.1%

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

   5. Taylor expanded in a around 0 74.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+29} \lor \neg \left(a \leq 3 \cdot 10^{+57}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 12: 76.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+29} \lor \neg \left(a \leq 4.6 \cdot 10^{+58}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.4e+29) (not (<= a 4.6e+58))) (+ x y) (+ x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.4e+29) || !(a <= 4.6e+58)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.4d+29)) .or. (.not. (a <= 4.6d+58))) then
        tmp = x + y
    else
        tmp = x + (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.4e+29) || !(a <= 4.6e+58)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.4e+29) or not (a <= 4.6e+58):
		tmp = x + y
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.4e+29) || !(a <= 4.6e+58))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.4e+29) || ~((a <= 4.6e+58)))
		tmp = x + y;
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.4e+29], N[Not[LessEqual[a, 4.6e+58]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.39999999999999981e29 or 4.60000000000000005e58 < a

   1. Initial program 80.3%

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

      1. associate--l+ 80.8%

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

      2. sub-neg 80.8%

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

      3. distribute-frac-neg 80.8%

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

      4. distribute-rgt-neg-out 80.8%

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

      5. +-commutative 80.8%

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

      6. distribute-rgt-neg-out 80.8%

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

      7. distribute-lft-neg-in 80.8%

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

      8. associate-/l* 90.2%

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

      9. associate-/r/ 91.9%

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

      10. fma-def 91.9%

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

      11. sub-neg 91.9%

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

      12. distribute-neg-in 91.9%

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

      13. remove-double-neg 91.9%

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

      14. +-commutative 91.9%

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

      15. sub-neg 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in a around inf 78.7%

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

      1. +-commutative 78.7%

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

   6. Simplified 78.7%

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

   if -3.39999999999999981e29 < a < 4.60000000000000005e58

   1. Initial program 78.1%

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

      1. associate--l+ 82.1%

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

      2. sub-neg 82.1%

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

      3. distribute-frac-neg 82.1%

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

      4. distribute-rgt-neg-out 82.1%

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

      5. +-commutative 82.1%

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

      6. distribute-rgt-neg-out 82.1%

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

      7. distribute-lft-neg-in 82.1%

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

      8. associate-/l* 86.0%

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

      9. associate-/r/ 87.1%

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

      10. fma-def 87.1%

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

      11. sub-neg 87.1%

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

      12. distribute-neg-in 87.1%

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

      13. remove-double-neg 87.1%

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

      14. +-commutative 87.1%

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

      15. sub-neg 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in y around 0 92.1%

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

   5. Taylor expanded in z around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. associate-*r* 87.1%

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

      3. neg-mul-1 87.1%

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

      4. *-commutative 87.1%

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

      5. associate-/l* 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in a around 0 74.5%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+29} \lor \neg \left(a \leq 4.6 \cdot 10^{+58}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 13: 74.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-75} \lor \neg \left(a \leq 9.8 \cdot 10^{+57}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.1e-75) (not (<= a 9.8e+57))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.1e-75) || !(a <= 9.8e+57)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.1d-75)) .or. (.not. (a <= 9.8d+57))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.1e-75) || !(a <= 9.8e+57)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.1e-75) or not (a <= 9.8e+57):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.1e-75) || !(a <= 9.8e+57))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.1e-75) || ~((a <= 9.8e+57)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.1e-75], N[Not[LessEqual[a, 9.8e+57]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.10000000000000002e-75 or 9.7999999999999998e57 < a

   1. Initial program 77.3%

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

      1. associate--l+ 78.7%

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

      2. sub-neg 78.7%

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

      3. distribute-frac-neg 78.7%

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

      4. distribute-rgt-neg-out 78.7%

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

      5. +-commutative 78.7%

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

      6. distribute-rgt-neg-out 78.7%

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

      7. distribute-lft-neg-in 78.7%

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

      8. associate-/l* 89.2%

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

      9. associate-/r/ 90.6%

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

      10. fma-def 90.6%

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

      11. sub-neg 90.6%

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

      12. distribute-neg-in 90.6%

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

      13. remove-double-neg 90.6%

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

      14. +-commutative 90.6%

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

      15. sub-neg 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 74.2%

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

      1. +-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -4.10000000000000002e-75 < a < 9.7999999999999998e57

   1. Initial program 80.3%

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

      1. associate--l+ 84.1%

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

      2. sub-neg 84.1%

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

      3. distribute-frac-neg 84.1%

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

      4. distribute-rgt-neg-out 84.1%

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

      5. +-commutative 84.1%

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

      6. distribute-rgt-neg-out 84.1%

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

      7. distribute-lft-neg-in 84.1%

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

      8. associate-/l* 86.4%

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

      9. associate-/r/ 87.6%

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

      10. fma-def 87.5%

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

      11. sub-neg 87.5%

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

      12. distribute-neg-in 87.5%

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

      13. remove-double-neg 87.5%

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

      14. +-commutative 87.5%

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

      15. sub-neg 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in y around 0 92.5%

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

   5. Taylor expanded in a around 0 77.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-75} \lor \neg \left(a \leq 9.8 \cdot 10^{+57}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 14: 60.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.9 \cdot 10^{+159}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 1.9e+159) (+ x y) (* y (/ z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.9e+159) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 1.9d+159) then
        tmp = x + y
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.9e+159) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.9e+159:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.9e+159)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.9e+159)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1.9e+159], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.89999999999999983e159

   1. Initial program 77.9%

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

      1. associate--l+ 80.9%

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

      2. sub-neg 80.9%

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

      3. distribute-frac-neg 80.9%

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

      4. distribute-rgt-neg-out 80.9%

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

      5. +-commutative 80.9%

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

      6. distribute-rgt-neg-out 80.9%

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

      7. distribute-lft-neg-in 80.9%

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

      8. associate-/l* 87.2%

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

      9. associate-/r/ 88.6%

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

      10. fma-def 88.6%

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

      11. sub-neg 88.6%

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

      12. distribute-neg-in 88.6%

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

      13. remove-double-neg 88.6%

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

      14. +-commutative 88.6%

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

      15. sub-neg 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 66.7%

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

      1. +-commutative 66.7%

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

   6. Simplified 66.7%

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

   if 1.89999999999999983e159 < z

   1. Initial program 88.5%

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

      1. +-commutative 88.5%

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

      2. associate--l+ 88.5%

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

      3. sub-neg 88.5%

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

      4. distribute-frac-neg 88.5%

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

      5. distribute-rgt-neg-out 88.5%

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

      6. distribute-rgt-neg-out 88.5%

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

      7. distribute-frac-neg 88.5%

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

      8. sub-neg 88.5%

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

      9. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

      1. div-inv 92.4%

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

   5. Applied egg-rr 92.4%

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

   6. Taylor expanded in z around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-*l/ 69.4%

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

      4. *-commutative 69.4%

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

      5. distribute-rgt-neg-in 69.4%

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

      6. distribute-neg-frac 69.4%

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

   8. Simplified 69.4%

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

   9. Taylor expanded in a around 0 48.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.9 \cdot 10^{+159}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 15: 61.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 5e+14) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5e+14) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 5d+14) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 5e+14) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 5e+14:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 5e+14)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 5e+14)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 5e+14], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < 5e14

   1. Initial program 83.7%

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

      1. associate--l+ 85.1%

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

      2. sub-neg 85.1%

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

      3. distribute-frac-neg 85.1%

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

      4. distribute-rgt-neg-out 85.1%

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

      5. +-commutative 85.1%

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

      6. distribute-rgt-neg-out 85.1%

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

      7. distribute-lft-neg-in 85.1%

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

      8. associate-/l* 90.7%

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

      9. associate-/r/ 90.2%

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

      10. fma-def 90.2%

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

      11. sub-neg 90.2%

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

      12. distribute-neg-in 90.2%

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

      13. remove-double-neg 90.2%

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

      14. +-commutative 90.2%

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

      15. sub-neg 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in a around inf 63.3%

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

      1. +-commutative 63.3%

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

   6. Simplified 63.3%

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

   if 5e14 < t

   1. Initial program 64.6%

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

      1. associate--l+ 71.1%

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

      2. sub-neg 71.1%

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

      3. distribute-frac-neg 71.1%

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

      4. distribute-rgt-neg-out 71.1%

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

      5. +-commutative 71.1%

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

      6. distribute-rgt-neg-out 71.1%

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

      7. distribute-lft-neg-in 71.1%

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

      8. associate-/l* 78.5%

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

      9. associate-/r/ 85.3%

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

      10. fma-def 85.2%

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

      11. sub-neg 85.2%

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

      12. distribute-neg-in 85.2%

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

      13. remove-double-neg 85.2%

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

      14. +-commutative 85.2%

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

      15. sub-neg 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around inf 68.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 51.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 78.9%

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

   1. associate--l+ 81.6%

      \[\leadsto \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]

   2. sub-neg 81.6%

      \[\leadsto x + \color{blue}{\left(y + \left(-\frac{\left(z - t\right) \cdot y}{a - t}\right)\right)} \]

   3. distribute-frac-neg 81.6%

      \[\leadsto x + \left(y + \color{blue}{\frac{-\left(z - t\right) \cdot y}{a - t}}\right) \]

   4. distribute-rgt-neg-out 81.6%

      \[\leadsto x + \left(y + \frac{\color{blue}{\left(z - t\right) \cdot \left(-y\right)}}{a - t}\right) \]

   5. +-commutative 81.6%

      \[\leadsto x + \color{blue}{\left(\frac{\left(z - t\right) \cdot \left(-y\right)}{a - t} + y\right)} \]

   6. distribute-rgt-neg-out 81.6%

      \[\leadsto x + \left(\frac{\color{blue}{-\left(z - t\right) \cdot y}}{a - t} + y\right) \]

   7. distribute-lft-neg-in 81.6%

      \[\leadsto x + \left(\frac{\color{blue}{\left(-\left(z - t\right)\right) \cdot y}}{a - t} + y\right) \]

   8. associate-/l* 87.7%

      \[\leadsto x + \left(\color{blue}{\frac{-\left(z - t\right)}{\frac{a - t}{y}}} + y\right) \]

   9. associate-/r/ 89.0%

      \[\leadsto x + \left(\color{blue}{\frac{-\left(z - t\right)}{a - t} \cdot y} + y\right) \]

   10. fma-def 88.9%

       \[\leadsto x + \color{blue}{\mathsf{fma}\left(\frac{-\left(z - t\right)}{a - t}, y, y\right)} \]

   11. sub-neg 88.9%

       \[\leadsto x + \mathsf{fma}\left(\frac{-\color{blue}{\left(z + \left(-t\right)\right)}}{a - t}, y, y\right) \]

   12. distribute-neg-in 88.9%

       \[\leadsto x + \mathsf{fma}\left(\frac{\color{blue}{\left(-z\right) + \left(-\left(-t\right)\right)}}{a - t}, y, y\right) \]

   13. remove-double-neg 88.9%

       \[\leadsto x + \mathsf{fma}\left(\frac{\left(-z\right) + \color{blue}{t}}{a - t}, y, y\right) \]

   14. +-commutative 88.9%

       \[\leadsto x + \mathsf{fma}\left(\frac{\color{blue}{t + \left(-z\right)}}{a - t}, y, y\right) \]

   15. sub-neg 88.9%

       \[\leadsto x + \mathsf{fma}\left(\frac{\color{blue}{t - z}}{a - t}, y, y\right) \]

3. Simplified 88.9%

   \[\leadsto \color{blue}{x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)} \]

4. Taylor expanded in x around inf 54.6%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 54.6%

   \[\leadsto x \]

Developer target: 87.7% 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 2023320 
(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))))