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

Percentage Accurate: 77.6% → 90.5%

Time: 15.8s

Alternatives: 11

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: 77.6% 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: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.12e+142)
   (+ x (* (/ (- z a) t) y))
   (+ x (* y (+ (/ (- t z) (- a t)) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.12e+142) {
		tmp = x + (((z - a) / t) * y);
	} else {
		tmp = x + (y * (((t - z) / (a - t)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.12d+142)) then
        tmp = x + (((z - a) / t) * y)
    else
        tmp = x + (y * (((t - z) / (a - t)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.12e+142) {
		tmp = x + (((z - a) / t) * y);
	} else {
		tmp = x + (y * (((t - z) / (a - t)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.12e+142:
		tmp = x + (((z - a) / t) * y)
	else:
		tmp = x + (y * (((t - z) / (a - t)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.12e+142)
		tmp = Float64(x + Float64(Float64(Float64(z - a) / t) * y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.12e+142)
		tmp = x + (((z - a) / t) * y);
	else
		tmp = x + (y * (((t - z) / (a - t)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.12e+142], N[(x + N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.11999999999999996e142

   1. Initial program 56.5%

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

      1. sub-neg 56.5%

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

      2. associate-+l+ 62.7%

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

      3. neg-mul-1 62.7%

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

      4. associate-*l/ 70.3%

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

      5. associate-*r* 70.3%

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

      6. distribute-rgt1-in 70.3%

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

      7. mul-1-neg 70.3%

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

      8. distribute-frac-neg 70.3%

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

      9. sub-neg 70.3%

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

      10. distribute-neg-in 70.3%

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

      11. remove-double-neg 70.3%

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

      12. +-commutative 70.3%

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

      13. sub-neg 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in t around -inf 93.8%

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

   if -1.11999999999999996e142 < t

   1. Initial program 79.4%

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

      1. sub-neg 79.4%

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

      2. associate-+l+ 82.6%

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

      3. neg-mul-1 82.6%

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

      4. associate-*l/ 92.6%

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

      5. associate-*r* 92.6%

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

      6. distribute-rgt1-in 92.6%

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

      7. mul-1-neg 92.6%

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

      8. distribute-frac-neg 92.6%

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

      9. sub-neg 92.6%

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

      10. distribute-neg-in 92.6%

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

      11. remove-double-neg 92.6%

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

      12. +-commutative 92.6%

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

      13. sub-neg 92.6%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{x + \left(\frac{t - z}{a - t} + 1\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \end{array} \]

Alternative 2: 77.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - a}{t} \cdot y\\ t_2 := x - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- z a) t) y))) (t_2 (- x (/ y (/ a z)))))
   (if (<= a -1.02e+139)
     (+ x y)
     (if (<= a -9.5e-40)
       t_2
       (if (<= a 1.55e-13)
         t_1
         (if (<= a 1.15e+54) t_2 (if (<= a 1.45e+140) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((z - a) / t) * y);
	double t_2 = x - (y / (a / z));
	double tmp;
	if (a <= -1.02e+139) {
		tmp = x + y;
	} else if (a <= -9.5e-40) {
		tmp = t_2;
	} else if (a <= 1.55e-13) {
		tmp = t_1;
	} else if (a <= 1.15e+54) {
		tmp = t_2;
	} else if (a <= 1.45e+140) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((z - a) / t) * y)
    t_2 = x - (y / (a / z))
    if (a <= (-1.02d+139)) then
        tmp = x + y
    else if (a <= (-9.5d-40)) then
        tmp = t_2
    else if (a <= 1.55d-13) then
        tmp = t_1
    else if (a <= 1.15d+54) then
        tmp = t_2
    else if (a <= 1.45d+140) then
        tmp = t_1
    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 t_1 = x + (((z - a) / t) * y);
	double t_2 = x - (y / (a / z));
	double tmp;
	if (a <= -1.02e+139) {
		tmp = x + y;
	} else if (a <= -9.5e-40) {
		tmp = t_2;
	} else if (a <= 1.55e-13) {
		tmp = t_1;
	} else if (a <= 1.15e+54) {
		tmp = t_2;
	} else if (a <= 1.45e+140) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((z - a) / t) * y)
	t_2 = x - (y / (a / z))
	tmp = 0
	if a <= -1.02e+139:
		tmp = x + y
	elif a <= -9.5e-40:
		tmp = t_2
	elif a <= 1.55e-13:
		tmp = t_1
	elif a <= 1.15e+54:
		tmp = t_2
	elif a <= 1.45e+140:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(z - a) / t) * y))
	t_2 = Float64(x - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.02e+139)
		tmp = Float64(x + y);
	elseif (a <= -9.5e-40)
		tmp = t_2;
	elseif (a <= 1.55e-13)
		tmp = t_1;
	elseif (a <= 1.15e+54)
		tmp = t_2;
	elseif (a <= 1.45e+140)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((z - a) / t) * y);
	t_2 = x - (y / (a / z));
	tmp = 0.0;
	if (a <= -1.02e+139)
		tmp = x + y;
	elseif (a <= -9.5e-40)
		tmp = t_2;
	elseif (a <= 1.55e-13)
		tmp = t_1;
	elseif (a <= 1.15e+54)
		tmp = t_2;
	elseif (a <= 1.45e+140)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.02e+139], N[(x + y), $MachinePrecision], If[LessEqual[a, -9.5e-40], t$95$2, If[LessEqual[a, 1.55e-13], t$95$1, If[LessEqual[a, 1.15e+54], t$95$2, If[LessEqual[a, 1.45e+140], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.02e139 or 1.4499999999999999e140 < a

   1. Initial program 76.2%

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

   2. Taylor expanded in a around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -1.02e139 < a < -9.5000000000000006e-40 or 1.55e-13 < a < 1.14999999999999997e54

   1. Initial program 85.1%

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

      1. sub-neg 85.1%

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

      2. associate-+l+ 87.5%

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

      3. neg-mul-1 87.5%

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

      4. associate-*l/ 97.7%

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

      5. associate-*r* 97.7%

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

      6. distribute-rgt1-in 97.7%

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

      7. mul-1-neg 97.7%

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

      8. distribute-frac-neg 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. remove-double-neg 97.7%

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

      12. +-commutative 97.7%

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

      13. sub-neg 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. associate-*r/ 86.4%

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

      2. mul-1-neg 86.4%

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

      3. *-commutative 86.4%

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

      4. distribute-lft-neg-out 86.4%

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

      5. mul-1-neg 86.4%

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

      6. associate-/l* 89.2%

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

      7. mul-1-neg 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in a around inf 78.0%

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

      1. associate-/l* 79.6%

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

      2. associate-*r/ 79.6%

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

      3. neg-mul-1 79.6%

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

   9. Simplified 79.6%

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

   if -9.5000000000000006e-40 < a < 1.55e-13 or 1.14999999999999997e54 < a < 1.4499999999999999e140

   1. Initial program 73.5%

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

      1. sub-neg 73.5%

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

      2. associate-+l+ 79.0%

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

      3. neg-mul-1 79.0%

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

      4. associate-*l/ 84.1%

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

      5. associate-*r* 84.1%

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

      6. distribute-rgt1-in 84.1%

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

      7. mul-1-neg 84.1%

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

      8. distribute-frac-neg 84.1%

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

      9. sub-neg 84.1%

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

      10. distribute-neg-in 84.1%

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

      11. remove-double-neg 84.1%

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

      12. +-commutative 84.1%

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

      13. sub-neg 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in t around -inf 86.4%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 77.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+139}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a z)))))
   (if (<= a -1.65e+139)
     (+ x y)
     (if (<= a -2.1e-39)
       t_1
       (if (<= a 1.2e-13)
         (+ x (/ y (/ t (- z a))))
         (if (<= a 2.1e+55)
           t_1
           (if (<= a 1.45e+140) (+ x (* (/ (- z a) t) y)) (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / z));
	double tmp;
	if (a <= -1.65e+139) {
		tmp = x + y;
	} else if (a <= -2.1e-39) {
		tmp = t_1;
	} else if (a <= 1.2e-13) {
		tmp = x + (y / (t / (z - a)));
	} else if (a <= 2.1e+55) {
		tmp = t_1;
	} else if (a <= 1.45e+140) {
		tmp = x + (((z - a) / t) * y);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (a / z))
    if (a <= (-1.65d+139)) then
        tmp = x + y
    else if (a <= (-2.1d-39)) then
        tmp = t_1
    else if (a <= 1.2d-13) then
        tmp = x + (y / (t / (z - a)))
    else if (a <= 2.1d+55) then
        tmp = t_1
    else if (a <= 1.45d+140) then
        tmp = x + (((z - a) / t) * y)
    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 t_1 = x - (y / (a / z));
	double tmp;
	if (a <= -1.65e+139) {
		tmp = x + y;
	} else if (a <= -2.1e-39) {
		tmp = t_1;
	} else if (a <= 1.2e-13) {
		tmp = x + (y / (t / (z - a)));
	} else if (a <= 2.1e+55) {
		tmp = t_1;
	} else if (a <= 1.45e+140) {
		tmp = x + (((z - a) / t) * y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / z))
	tmp = 0
	if a <= -1.65e+139:
		tmp = x + y
	elif a <= -2.1e-39:
		tmp = t_1
	elif a <= 1.2e-13:
		tmp = x + (y / (t / (z - a)))
	elif a <= 2.1e+55:
		tmp = t_1
	elif a <= 1.45e+140:
		tmp = x + (((z - a) / t) * y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.65e+139)
		tmp = Float64(x + y);
	elseif (a <= -2.1e-39)
		tmp = t_1;
	elseif (a <= 1.2e-13)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	elseif (a <= 2.1e+55)
		tmp = t_1;
	elseif (a <= 1.45e+140)
		tmp = Float64(x + Float64(Float64(Float64(z - a) / t) * y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / z));
	tmp = 0.0;
	if (a <= -1.65e+139)
		tmp = x + y;
	elseif (a <= -2.1e-39)
		tmp = t_1;
	elseif (a <= 1.2e-13)
		tmp = x + (y / (t / (z - a)));
	elseif (a <= 2.1e+55)
		tmp = t_1;
	elseif (a <= 1.45e+140)
		tmp = x + (((z - a) / t) * y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+139], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.1e-39], t$95$1, If[LessEqual[a, 1.2e-13], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+55], t$95$1, If[LessEqual[a, 1.45e+140], N[(x + N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6500000000000001e139 or 1.4499999999999999e140 < a

   1. Initial program 76.2%

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

   2. Taylor expanded in a around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -1.6500000000000001e139 < a < -2.09999999999999993e-39 or 1.1999999999999999e-13 < a < 2.1000000000000001e55

   1. Initial program 85.1%

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

      1. sub-neg 85.1%

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

      2. associate-+l+ 87.5%

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

      3. neg-mul-1 87.5%

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

      4. associate-*l/ 97.7%

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

      5. associate-*r* 97.7%

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

      6. distribute-rgt1-in 97.7%

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

      7. mul-1-neg 97.7%

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

      8. distribute-frac-neg 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. remove-double-neg 97.7%

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

      12. +-commutative 97.7%

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

      13. sub-neg 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. associate-*r/ 86.4%

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

      2. mul-1-neg 86.4%

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

      3. *-commutative 86.4%

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

      4. distribute-lft-neg-out 86.4%

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

      5. mul-1-neg 86.4%

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

      6. associate-/l* 89.2%

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

      7. mul-1-neg 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in a around inf 78.0%

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

      1. associate-/l* 79.6%

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

      2. associate-*r/ 79.6%

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

      3. neg-mul-1 79.6%

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

   9. Simplified 79.6%

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

   if -2.09999999999999993e-39 < a < 1.1999999999999999e-13

   1. Initial program 76.1%

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

      1. sub-neg 76.1%

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

      2. associate-+l+ 82.2%

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

      3. neg-mul-1 82.2%

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

      4. associate-*l/ 84.8%

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

      5. associate-*r* 84.8%

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

      6. distribute-rgt1-in 84.8%

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

      7. mul-1-neg 84.8%

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

      8. distribute-frac-neg 84.8%

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

      9. sub-neg 84.8%

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

      10. distribute-neg-in 84.8%

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

      11. remove-double-neg 84.8%

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

      12. +-commutative 84.8%

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

      13. sub-neg 84.8%

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

   3. Simplified 84.8%

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

      1. div-inv 83.9%

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

      2. *-commutative 83.9%

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

   5. Applied egg-rr 83.9%

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

   6. Taylor expanded in t around -inf 86.0%

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

      1. associate-/l* 87.5%

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

   8. Simplified 87.5%

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

   if 2.1000000000000001e55 < a < 1.4499999999999999e140

   1. Initial program 48.4%

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

      1. sub-neg 48.4%

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

      2. associate-+l+ 48.6%

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

      3. neg-mul-1 48.6%

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

      4. associate-*l/ 77.8%

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

      5. associate-*r* 77.8%

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

      6. distribute-rgt1-in 77.8%

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

      7. mul-1-neg 77.8%

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

      8. distribute-frac-neg 77.8%

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

      9. sub-neg 77.8%

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

      10. distribute-neg-in 77.8%

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

      11. remove-double-neg 77.8%

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

      12. +-commutative 77.8%

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

      13. sub-neg 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in t around -inf 78.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+139}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-39}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 77.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+139}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a z)))))
   (if (<= a -3.7e+139)
     (+ x y)
     (if (<= a -6.2e-40)
       t_1
       (if (<= a 9.5e-14)
         (+ x (/ y (/ t (- z a))))
         (if (<= a 2.3e+54)
           t_1
           (if (<= a 1.45e+140) (+ x (/ (- z a) (/ t y))) (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / z));
	double tmp;
	if (a <= -3.7e+139) {
		tmp = x + y;
	} else if (a <= -6.2e-40) {
		tmp = t_1;
	} else if (a <= 9.5e-14) {
		tmp = x + (y / (t / (z - a)));
	} else if (a <= 2.3e+54) {
		tmp = t_1;
	} else if (a <= 1.45e+140) {
		tmp = x + ((z - a) / (t / y));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (a / z))
    if (a <= (-3.7d+139)) then
        tmp = x + y
    else if (a <= (-6.2d-40)) then
        tmp = t_1
    else if (a <= 9.5d-14) then
        tmp = x + (y / (t / (z - a)))
    else if (a <= 2.3d+54) then
        tmp = t_1
    else if (a <= 1.45d+140) then
        tmp = x + ((z - a) / (t / y))
    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 t_1 = x - (y / (a / z));
	double tmp;
	if (a <= -3.7e+139) {
		tmp = x + y;
	} else if (a <= -6.2e-40) {
		tmp = t_1;
	} else if (a <= 9.5e-14) {
		tmp = x + (y / (t / (z - a)));
	} else if (a <= 2.3e+54) {
		tmp = t_1;
	} else if (a <= 1.45e+140) {
		tmp = x + ((z - a) / (t / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / z))
	tmp = 0
	if a <= -3.7e+139:
		tmp = x + y
	elif a <= -6.2e-40:
		tmp = t_1
	elif a <= 9.5e-14:
		tmp = x + (y / (t / (z - a)))
	elif a <= 2.3e+54:
		tmp = t_1
	elif a <= 1.45e+140:
		tmp = x + ((z - a) / (t / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -3.7e+139)
		tmp = Float64(x + y);
	elseif (a <= -6.2e-40)
		tmp = t_1;
	elseif (a <= 9.5e-14)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	elseif (a <= 2.3e+54)
		tmp = t_1;
	elseif (a <= 1.45e+140)
		tmp = Float64(x + Float64(Float64(z - a) / Float64(t / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / z));
	tmp = 0.0;
	if (a <= -3.7e+139)
		tmp = x + y;
	elseif (a <= -6.2e-40)
		tmp = t_1;
	elseif (a <= 9.5e-14)
		tmp = x + (y / (t / (z - a)));
	elseif (a <= 2.3e+54)
		tmp = t_1;
	elseif (a <= 1.45e+140)
		tmp = x + ((z - a) / (t / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+139], N[(x + y), $MachinePrecision], If[LessEqual[a, -6.2e-40], t$95$1, If[LessEqual[a, 9.5e-14], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+54], t$95$1, If[LessEqual[a, 1.45e+140], N[(x + N[(N[(z - a), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.69999999999999992e139 or 1.4499999999999999e140 < a

   1. Initial program 76.2%

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

   2. Taylor expanded in a around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -3.69999999999999992e139 < a < -6.20000000000000021e-40 or 9.4999999999999999e-14 < a < 2.29999999999999994e54

   1. Initial program 85.1%

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

      1. sub-neg 85.1%

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

      2. associate-+l+ 87.5%

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

      3. neg-mul-1 87.5%

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

      4. associate-*l/ 97.7%

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

      5. associate-*r* 97.7%

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

      6. distribute-rgt1-in 97.7%

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

      7. mul-1-neg 97.7%

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

      8. distribute-frac-neg 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. remove-double-neg 97.7%

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

      12. +-commutative 97.7%

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

      13. sub-neg 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. associate-*r/ 86.4%

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

      2. mul-1-neg 86.4%

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

      3. *-commutative 86.4%

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

      4. distribute-lft-neg-out 86.4%

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

      5. mul-1-neg 86.4%

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

      6. associate-/l* 89.2%

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

      7. mul-1-neg 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in a around inf 78.0%

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

      1. associate-/l* 79.6%

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

      2. associate-*r/ 79.6%

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

      3. neg-mul-1 79.6%

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

   9. Simplified 79.6%

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

   if -6.20000000000000021e-40 < a < 9.4999999999999999e-14

   1. Initial program 76.1%

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

      1. sub-neg 76.1%

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

      2. associate-+l+ 82.2%

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

      3. neg-mul-1 82.2%

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

      4. associate-*l/ 84.8%

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

      5. associate-*r* 84.8%

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

      6. distribute-rgt1-in 84.8%

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

      7. mul-1-neg 84.8%

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

      8. distribute-frac-neg 84.8%

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

      9. sub-neg 84.8%

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

      10. distribute-neg-in 84.8%

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

      11. remove-double-neg 84.8%

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

      12. +-commutative 84.8%

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

      13. sub-neg 84.8%

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

   3. Simplified 84.8%

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

      1. div-inv 83.9%

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

      2. *-commutative 83.9%

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

   5. Applied egg-rr 83.9%

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

   6. Taylor expanded in t around -inf 86.0%

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

      1. associate-/l* 87.5%

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

   8. Simplified 87.5%

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

   if 2.29999999999999994e54 < a < 1.4499999999999999e140

   1. Initial program 48.4%

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

      1. sub-neg 48.4%

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

      2. associate-+l+ 48.6%

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

      3. neg-mul-1 48.6%

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

      4. associate-*l/ 77.8%

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

      5. associate-*r* 77.8%

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

      6. distribute-rgt1-in 77.8%

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

      7. mul-1-neg 77.8%

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

      8. distribute-frac-neg 77.8%

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

      9. sub-neg 77.8%

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

      10. distribute-neg-in 77.8%

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

      11. remove-double-neg 77.8%

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

      12. +-commutative 77.8%

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

      13. sub-neg 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in t around -inf 56.5%

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

      1. *-commutative 56.5%

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

      2. associate-/l* 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+139}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -0.0075:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+88} \lor \neg \left(a \leq 3.1 \cdot 10^{+126}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ y (/ a z)))))
   (if (<= a -0.0075)
     t_1
     (if (<= a 1.25e-13)
       (+ x (/ y (/ t (- z a))))
       (if (or (<= a 3.7e+88) (not (<= a 3.1e+126)))
         t_1
         (+ x (* (/ (- z a) t) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y / (a / z));
	double tmp;
	if (a <= -0.0075) {
		tmp = t_1;
	} else if (a <= 1.25e-13) {
		tmp = x + (y / (t / (z - a)));
	} else if ((a <= 3.7e+88) || !(a <= 3.1e+126)) {
		tmp = t_1;
	} else {
		tmp = x + (((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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (y / (a / z))
    if (a <= (-0.0075d0)) then
        tmp = t_1
    else if (a <= 1.25d-13) then
        tmp = x + (y / (t / (z - a)))
    else if ((a <= 3.7d+88) .or. (.not. (a <= 3.1d+126))) then
        tmp = t_1
    else
        tmp = x + (((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 t_1 = (x + y) - (y / (a / z));
	double tmp;
	if (a <= -0.0075) {
		tmp = t_1;
	} else if (a <= 1.25e-13) {
		tmp = x + (y / (t / (z - a)));
	} else if ((a <= 3.7e+88) || !(a <= 3.1e+126)) {
		tmp = t_1;
	} else {
		tmp = x + (((z - a) / t) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y / (a / z))
	tmp = 0
	if a <= -0.0075:
		tmp = t_1
	elif a <= 1.25e-13:
		tmp = x + (y / (t / (z - a)))
	elif (a <= 3.7e+88) or not (a <= 3.1e+126):
		tmp = t_1
	else:
		tmp = x + (((z - a) / t) * y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -0.0075)
		tmp = t_1;
	elseif (a <= 1.25e-13)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	elseif ((a <= 3.7e+88) || !(a <= 3.1e+126))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(Float64(z - a) / t) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y / (a / z));
	tmp = 0.0;
	if (a <= -0.0075)
		tmp = t_1;
	elseif (a <= 1.25e-13)
		tmp = x + (y / (t / (z - a)));
	elseif ((a <= 3.7e+88) || ~((a <= 3.1e+126)))
		tmp = t_1;
	else
		tmp = x + (((z - a) / t) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0075], t$95$1, If[LessEqual[a, 1.25e-13], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 3.7e+88], N[Not[LessEqual[a, 3.1e+126]], $MachinePrecision]], t$95$1, N[(x + N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.0074999999999999997 or 1.24999999999999997e-13 < a < 3.69999999999999994e88 or 3.1e126 < a

   1. Initial program 80.6%

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

   2. Taylor expanded in t around 0 81.9%

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

      1. associate-/l* 89.9%

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

   4. Simplified 89.9%

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

   if -0.0074999999999999997 < a < 1.24999999999999997e-13

   1. Initial program 75.8%

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

      1. sub-neg 75.8%

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

      2. associate-+l+ 81.8%

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

      3. neg-mul-1 81.8%

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

      4. associate-*l/ 85.7%

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

      5. associate-*r* 85.7%

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

      6. distribute-rgt1-in 85.7%

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

      7. mul-1-neg 85.7%

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

      8. distribute-frac-neg 85.7%

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

      9. sub-neg 85.7%

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

      10. distribute-neg-in 85.7%

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

      11. remove-double-neg 85.7%

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

      12. +-commutative 85.7%

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

      13. sub-neg 85.7%

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

   3. Simplified 85.7%

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

      1. div-inv 84.9%

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

      2. *-commutative 84.9%

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

   5. Applied egg-rr 84.9%

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

   6. Taylor expanded in t around -inf 84.7%

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

      1. associate-/l* 86.1%

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

   8. Simplified 86.1%

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

   if 3.69999999999999994e88 < a < 3.1e126

   1. Initial program 30.0%

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

      1. sub-neg 30.0%

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

      2. associate-+l+ 30.4%

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

      3. neg-mul-1 30.4%

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

      4. associate-*l/ 58.9%

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

      5. associate-*r* 58.9%

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

      6. distribute-rgt1-in 58.9%

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

      7. mul-1-neg 58.9%

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

      8. distribute-frac-neg 58.9%

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

      9. sub-neg 58.9%

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

      10. distribute-neg-in 58.9%

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

      11. remove-double-neg 58.9%

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

      12. +-commutative 58.9%

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

      13. sub-neg 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in t around -inf 100.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0075:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+88} \lor \neg \left(a \leq 3.1 \cdot 10^{+126}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \end{array} \]

Alternative 6: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+88}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ y (/ a z)))))
   (if (<= a -1.45e-5)
     t_1
     (if (<= a 1.35e-13)
       (+ x (/ y (/ t (- z a))))
       (if (<= a 4e+88)
         (- (+ x y) (/ z (/ a y)))
         (if (<= a 3.1e+126) (+ x (* (/ (- z a) t) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y / (a / z));
	double tmp;
	if (a <= -1.45e-5) {
		tmp = t_1;
	} else if (a <= 1.35e-13) {
		tmp = x + (y / (t / (z - a)));
	} else if (a <= 4e+88) {
		tmp = (x + y) - (z / (a / y));
	} else if (a <= 3.1e+126) {
		tmp = x + (((z - a) / t) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (y / (a / z))
    if (a <= (-1.45d-5)) then
        tmp = t_1
    else if (a <= 1.35d-13) then
        tmp = x + (y / (t / (z - a)))
    else if (a <= 4d+88) then
        tmp = (x + y) - (z / (a / y))
    else if (a <= 3.1d+126) then
        tmp = x + (((z - a) / t) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y / (a / z));
	double tmp;
	if (a <= -1.45e-5) {
		tmp = t_1;
	} else if (a <= 1.35e-13) {
		tmp = x + (y / (t / (z - a)));
	} else if (a <= 4e+88) {
		tmp = (x + y) - (z / (a / y));
	} else if (a <= 3.1e+126) {
		tmp = x + (((z - a) / t) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y / (a / z))
	tmp = 0
	if a <= -1.45e-5:
		tmp = t_1
	elif a <= 1.35e-13:
		tmp = x + (y / (t / (z - a)))
	elif a <= 4e+88:
		tmp = (x + y) - (z / (a / y))
	elif a <= 3.1e+126:
		tmp = x + (((z - a) / t) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.45e-5)
		tmp = t_1;
	elseif (a <= 1.35e-13)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	elseif (a <= 4e+88)
		tmp = Float64(Float64(x + y) - Float64(z / Float64(a / y)));
	elseif (a <= 3.1e+126)
		tmp = Float64(x + Float64(Float64(Float64(z - a) / t) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y / (a / z));
	tmp = 0.0;
	if (a <= -1.45e-5)
		tmp = t_1;
	elseif (a <= 1.35e-13)
		tmp = x + (y / (t / (z - a)));
	elseif (a <= 4e+88)
		tmp = (x + y) - (z / (a / y));
	elseif (a <= 3.1e+126)
		tmp = x + (((z - a) / t) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e-5], t$95$1, If[LessEqual[a, 1.35e-13], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+88], N[(N[(x + y), $MachinePrecision] - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+126], N[(x + N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45e-5 or 3.1e126 < a

   1. Initial program 79.3%

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

   2. Taylor expanded in t around 0 81.0%

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

      1. associate-/l* 90.8%

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

   4. Simplified 90.8%

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

   if -1.45e-5 < a < 1.35000000000000005e-13

   1. Initial program 75.8%

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

      1. sub-neg 75.8%

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

      2. associate-+l+ 81.8%

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

      3. neg-mul-1 81.8%

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

      4. associate-*l/ 85.7%

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

      5. associate-*r* 85.7%

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

      6. distribute-rgt1-in 85.7%

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

      7. mul-1-neg 85.7%

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

      8. distribute-frac-neg 85.7%

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

      9. sub-neg 85.7%

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

      10. distribute-neg-in 85.7%

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

      11. remove-double-neg 85.7%

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

      12. +-commutative 85.7%

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

      13. sub-neg 85.7%

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

   3. Simplified 85.7%

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

      1. div-inv 84.9%

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

      2. *-commutative 84.9%

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

   5. Applied egg-rr 84.9%

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

   6. Taylor expanded in t around -inf 84.7%

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

      1. associate-/l* 86.1%

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

   8. Simplified 86.1%

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

   if 1.35000000000000005e-13 < a < 3.99999999999999984e88

   1. Initial program 86.5%

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

   2. Taylor expanded in t around 0 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-/l* 85.8%

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

   4. Simplified 85.8%

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

   if 3.99999999999999984e88 < a < 3.1e126

   1. Initial program 30.0%

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

      1. sub-neg 30.0%

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

      2. associate-+l+ 30.4%

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

      3. neg-mul-1 30.4%

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

      4. associate-*l/ 58.9%

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

      5. associate-*r* 58.9%

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

      6. distribute-rgt1-in 58.9%

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

      7. mul-1-neg 58.9%

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

      8. distribute-frac-neg 58.9%

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

      9. sub-neg 58.9%

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

      10. distribute-neg-in 58.9%

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

      11. remove-double-neg 58.9%

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

      12. +-commutative 58.9%

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

      13. sub-neg 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in t around -inf 100.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-5}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+88}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{z - a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+136)
   (+ x y)
   (if (<= a -7e-40)
     (- x (/ y (/ a z)))
     (if (<= a 1.45e+140) (+ x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+136) {
		tmp = x + y;
	} else if (a <= -7e-40) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.45e+140) {
		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 <= (-7d+136)) then
        tmp = x + y
    else if (a <= (-7d-40)) then
        tmp = x - (y / (a / z))
    else if (a <= 1.45d+140) 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 <= -7e+136) {
		tmp = x + y;
	} else if (a <= -7e-40) {
		tmp = x - (y / (a / z));
	} else if (a <= 1.45e+140) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+136:
		tmp = x + y
	elif a <= -7e-40:
		tmp = x - (y / (a / z))
	elif a <= 1.45e+140:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+136)
		tmp = Float64(x + y);
	elseif (a <= -7e-40)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (a <= 1.45e+140)
		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 <= -7e+136)
		tmp = x + y;
	elseif (a <= -7e-40)
		tmp = x - (y / (a / z));
	elseif (a <= 1.45e+140)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+136], N[(x + y), $MachinePrecision], If[LessEqual[a, -7e-40], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+140], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.00000000000000002e136 or 1.4499999999999999e140 < a

   1. Initial program 76.2%

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

   2. Taylor expanded in a around inf 83.6%

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

      1. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   if -7.00000000000000002e136 < a < -7.0000000000000003e-40

   1. Initial program 83.5%

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

      1. sub-neg 83.5%

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

      2. associate-+l+ 86.9%

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

      3. neg-mul-1 86.9%

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

      4. associate-*l/ 96.8%

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

      5. associate-*r* 96.8%

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

      6. distribute-rgt1-in 96.8%

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

      7. mul-1-neg 96.8%

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

      8. distribute-frac-neg 96.8%

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

      9. sub-neg 96.8%

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

      10. distribute-neg-in 96.8%

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

      11. remove-double-neg 96.8%

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

      12. +-commutative 96.8%

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

      13. sub-neg 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 89.9%

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

      1. associate-*r/ 89.9%

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

      2. mul-1-neg 89.9%

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

      3. *-commutative 89.9%

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

      4. distribute-lft-neg-out 89.9%

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

      5. mul-1-neg 89.9%

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

      6. associate-/l* 91.6%

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

      7. mul-1-neg 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in a around inf 80.5%

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

      1. associate-/l* 82.9%

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

      2. associate-*r/ 82.9%

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

      3. neg-mul-1 82.9%

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

   9. Simplified 82.9%

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

   if -7.0000000000000003e-40 < a < 1.4499999999999999e140

   1. Initial program 75.2%

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

      1. sub-neg 75.2%

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

      2. associate-+l+ 80.1%

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

      3. neg-mul-1 80.1%

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

      4. associate-*l/ 85.9%

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

      5. associate-*r* 85.9%

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

      6. distribute-rgt1-in 85.9%

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

      7. mul-1-neg 85.9%

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

      8. distribute-frac-neg 85.9%

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

      9. sub-neg 85.9%

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

      10. distribute-neg-in 85.9%

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

      11. remove-double-neg 85.9%

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

      12. +-commutative 85.9%

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

      13. sub-neg 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in a around 0 79.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+137} \lor \neg \left(a \leq 1.68 \cdot 10^{+128}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.4e+137) (not (<= a 1.68e+128)))
   (- (+ x y) (/ y (/ a z)))
   (- x (/ z (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.4e+137) || !(a <= 1.68e+128)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x - (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 ((a <= (-2.4d+137)) .or. (.not. (a <= 1.68d+128))) then
        tmp = (x + y) - (y / (a / z))
    else
        tmp = x - (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 ((a <= -2.4e+137) || !(a <= 1.68e+128)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x - (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.4e+137) or not (a <= 1.68e+128):
		tmp = (x + y) - (y / (a / z))
	else:
		tmp = x - (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.4e+137) || !(a <= 1.68e+128))
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x - Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.4e+137) || ~((a <= 1.68e+128)))
		tmp = (x + y) - (y / (a / z));
	else
		tmp = x - (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.4e+137], N[Not[LessEqual[a, 1.68e+128]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.39999999999999983e137 or 1.67999999999999993e128 < a

   1. Initial program 76.6%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. associate-/l* 92.2%

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

   4. Simplified 92.2%

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

   if -2.39999999999999983e137 < a < 1.67999999999999993e128

   1. Initial program 76.8%

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

      1. sub-neg 76.8%

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

      2. associate-+l+ 81.4%

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

      3. neg-mul-1 81.4%

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

      4. associate-*l/ 88.0%

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

      5. associate-*r* 88.0%

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

      6. distribute-rgt1-in 88.1%

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

      7. mul-1-neg 88.1%

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

      8. distribute-frac-neg 88.1%

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

      9. sub-neg 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. remove-double-neg 88.1%

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

      12. +-commutative 88.1%

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

      13. sub-neg 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around inf 85.4%

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

      1. associate-*r/ 85.4%

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

      2. mul-1-neg 85.4%

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

      3. *-commutative 85.4%

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

      4. distribute-lft-neg-out 85.4%

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

      5. mul-1-neg 85.4%

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

      6. associate-/l* 87.5%

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

      7. mul-1-neg 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+137} \lor \neg \left(a \leq 1.68 \cdot 10^{+128}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 9: 74.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+96} \lor \neg \left(a \leq 5.4 \cdot 10^{+142}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.6e+96) (not (<= a 5.4e+142))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.6e+96) || !(a <= 5.4e+142)) {
		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 <= (-7.6d+96)) .or. (.not. (a <= 5.4d+142))) 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 <= -7.6e+96) || !(a <= 5.4e+142)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.6e+96) or not (a <= 5.4e+142):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.6e+96) || !(a <= 5.4e+142))
		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 <= -7.6e+96) || ~((a <= 5.4e+142)))
		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, -7.6e+96], N[Not[LessEqual[a, 5.4e+142]], $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 < -7.6000000000000003e96 or 5.39999999999999965e142 < a

   1. Initial program 76.6%

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

   2. Taylor expanded in a around inf 82.9%

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

      1. +-commutative 82.9%

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

   4. Simplified 82.9%

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

   if -7.6000000000000003e96 < a < 5.39999999999999965e142

   1. Initial program 76.8%

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

      1. sub-neg 76.8%

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

      2. associate-+l+ 81.6%

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

      3. neg-mul-1 81.6%

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

      4. associate-*l/ 88.1%

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

      5. associate-*r* 88.1%

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

      6. distribute-rgt1-in 88.1%

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

      7. mul-1-neg 88.1%

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

      8. distribute-frac-neg 88.1%

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

      9. sub-neg 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. remove-double-neg 88.1%

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

      12. +-commutative 88.1%

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

      13. sub-neg 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in a around 0 75.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+96} \lor \neg \left(a \leq 5.4 \cdot 10^{+142}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 10: 61.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.1 \cdot 10^{+174}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 2.1e+174) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.1e+174) {
		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 <= 2.1d+174) 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 <= 2.1e+174) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.1e+174:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.1e+174)
		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 <= 2.1e+174)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.1e+174], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < 2.10000000000000017e174

   1. Initial program 82.5%

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

   2. Taylor expanded in a around inf 62.7%

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

      1. +-commutative 62.7%

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

   4. Simplified 62.7%

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

   if 2.10000000000000017e174 < t

   1. Initial program 32.0%

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

   2. Taylor expanded in x around inf 68.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.1 \cdot 10^{+174}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 50.8% 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 76.7%

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

2. Taylor expanded in x around inf 53.7%

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

3. Final simplification 53.7%

   \[\leadsto x \]

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 2023301 
(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))))