Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.2% → 98.2%

Time: 11.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-/l* 98.8%

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

3. Simplified 98.8%

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

   1. clear-num 98.8%

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

   2. associate-/r/ 98.8%

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

   3. clear-num 98.9%

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

6. Applied egg-rr 98.9%

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

7. Final simplification 98.9%

   \[\leadsto x + \frac{z - t}{z - a} \cdot y \]
8. Add Preprocessing

Alternative 2: 75.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-174}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= a -2.6e+42)
     (+ x (/ y (/ a t)))
     (if (<= a -8.2e-24)
       t_1
       (if (<= a -1e-55)
         (* t (/ (- y) (- z a)))
         (if (<= a -5.3e-174)
           (+ x y)
           (if (<= a 3.2e-117) t_1 (+ x (* y (/ t a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (a <= -2.6e+42) {
		tmp = x + (y / (a / t));
	} else if (a <= -8.2e-24) {
		tmp = t_1;
	} else if (a <= -1e-55) {
		tmp = t * (-y / (z - a));
	} else if (a <= -5.3e-174) {
		tmp = x + y;
	} else if (a <= 3.2e-117) {
		tmp = t_1;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (a <= (-2.6d+42)) then
        tmp = x + (y / (a / t))
    else if (a <= (-8.2d-24)) then
        tmp = t_1
    else if (a <= (-1d-55)) then
        tmp = t * (-y / (z - a))
    else if (a <= (-5.3d-174)) then
        tmp = x + y
    else if (a <= 3.2d-117) then
        tmp = t_1
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (a <= -2.6e+42) {
		tmp = x + (y / (a / t));
	} else if (a <= -8.2e-24) {
		tmp = t_1;
	} else if (a <= -1e-55) {
		tmp = t * (-y / (z - a));
	} else if (a <= -5.3e-174) {
		tmp = x + y;
	} else if (a <= 3.2e-117) {
		tmp = t_1;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if a <= -2.6e+42:
		tmp = x + (y / (a / t))
	elif a <= -8.2e-24:
		tmp = t_1
	elif a <= -1e-55:
		tmp = t * (-y / (z - a))
	elif a <= -5.3e-174:
		tmp = x + y
	elif a <= 3.2e-117:
		tmp = t_1
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (a <= -2.6e+42)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (a <= -8.2e-24)
		tmp = t_1;
	elseif (a <= -1e-55)
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - a)));
	elseif (a <= -5.3e-174)
		tmp = Float64(x + y);
	elseif (a <= 3.2e-117)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (a <= -2.6e+42)
		tmp = x + (y / (a / t));
	elseif (a <= -8.2e-24)
		tmp = t_1;
	elseif (a <= -1e-55)
		tmp = t * (-y / (z - a));
	elseif (a <= -5.3e-174)
		tmp = x + y;
	elseif (a <= 3.2e-117)
		tmp = t_1;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+42], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-24], t$95$1, If[LessEqual[a, -1e-55], N[(t * N[((-y) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.3e-174], N[(x + y), $MachinePrecision], If[LessEqual[a, 3.2e-117], t$95$1, N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.5999999999999999e42

   1. Initial program 92.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.7%

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

   if -2.5999999999999999e42 < a < -8.20000000000000029e-24 or -5.2999999999999996e-174 < a < 3.19999999999999995e-117

   1. Initial program 94.1%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

      1. clear-num 97.5%

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

      2. associate-/r/ 97.7%

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

      3. clear-num 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in a around 0 92.7%

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

   8. Taylor expanded in z around 0 92.7%

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

      1. neg-mul-1 92.7%

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

      2. sub-neg 92.7%

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

   10. Simplified 92.7%

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

   if -8.20000000000000029e-24 < a < -9.99999999999999995e-56

   1. Initial program 99.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.2%

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

      3. clear-num 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in t around inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. associate-*r* 99.6%

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

      3. neg-mul-1 99.6%

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

   9. Simplified 99.6%

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

       1. div-inv 99.2%

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

       2. add-sqr-sqrt 73.6%

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

       3. sqrt-unprod 74.7%

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

       4. sqr-neg 74.7%

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

       5. sqrt-unprod 0.1%

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

       6. add-sqr-sqrt 0.7%

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

       7. distribute-lft-neg-in 0.7%

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

       8. cancel-sign-sub-inv 0.7%

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

       9. div-inv 0.7%

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

       10. associate-/l* 0.7%

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

       11. add-sqr-sqrt 0.1%

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

       12. sqrt-unprod 74.7%

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

       13. sqr-neg 74.7%

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

       14. sqrt-unprod 73.6%

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

       15. add-sqr-sqrt 99.6%

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

   11. Applied egg-rr 99.6%

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

   12. Taylor expanded in x around 0 99.6%

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

       1. mul-1-neg 99.6%

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

       2. associate-*r/ 99.6%

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

       3. *-commutative 99.6%

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

       4. distribute-rgt-neg-in 99.6%

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

   14. Simplified 99.6%

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

   if -9.99999999999999995e-56 < a < -5.2999999999999996e-174

   1. Initial program 79.1%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 97.2%

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

      1. +-commutative 97.2%

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

   7. Simplified 97.2%

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

   if 3.19999999999999995e-117 < a

   1. Initial program 90.7%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. associate-/l* 80.7%

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

   7. Simplified 80.7%

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

      1. associate-/r/ 82.0%

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

   9. Applied egg-rr 82.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-174}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-174}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= a -2.8e+41)
     (+ x (/ y (/ a t)))
     (if (<= a -8.2e-24)
       t_1
       (if (<= a -3.7e-58)
         (* t (/ (- y) (- z a)))
         (if (<= a -3.4e-174)
           (+ x (* z (/ y (- z a))))
           (if (<= a 3.2e-117) t_1 (+ x (* y (/ t a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (a <= -2.8e+41) {
		tmp = x + (y / (a / t));
	} else if (a <= -8.2e-24) {
		tmp = t_1;
	} else if (a <= -3.7e-58) {
		tmp = t * (-y / (z - a));
	} else if (a <= -3.4e-174) {
		tmp = x + (z * (y / (z - a)));
	} else if (a <= 3.2e-117) {
		tmp = t_1;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (a <= (-2.8d+41)) then
        tmp = x + (y / (a / t))
    else if (a <= (-8.2d-24)) then
        tmp = t_1
    else if (a <= (-3.7d-58)) then
        tmp = t * (-y / (z - a))
    else if (a <= (-3.4d-174)) then
        tmp = x + (z * (y / (z - a)))
    else if (a <= 3.2d-117) then
        tmp = t_1
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (a <= -2.8e+41) {
		tmp = x + (y / (a / t));
	} else if (a <= -8.2e-24) {
		tmp = t_1;
	} else if (a <= -3.7e-58) {
		tmp = t * (-y / (z - a));
	} else if (a <= -3.4e-174) {
		tmp = x + (z * (y / (z - a)));
	} else if (a <= 3.2e-117) {
		tmp = t_1;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if a <= -2.8e+41:
		tmp = x + (y / (a / t))
	elif a <= -8.2e-24:
		tmp = t_1
	elif a <= -3.7e-58:
		tmp = t * (-y / (z - a))
	elif a <= -3.4e-174:
		tmp = x + (z * (y / (z - a)))
	elif a <= 3.2e-117:
		tmp = t_1
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (a <= -2.8e+41)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (a <= -8.2e-24)
		tmp = t_1;
	elseif (a <= -3.7e-58)
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - a)));
	elseif (a <= -3.4e-174)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (a <= 3.2e-117)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (a <= -2.8e+41)
		tmp = x + (y / (a / t));
	elseif (a <= -8.2e-24)
		tmp = t_1;
	elseif (a <= -3.7e-58)
		tmp = t * (-y / (z - a));
	elseif (a <= -3.4e-174)
		tmp = x + (z * (y / (z - a)));
	elseif (a <= 3.2e-117)
		tmp = t_1;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+41], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-24], t$95$1, If[LessEqual[a, -3.7e-58], N[(t * N[((-y) / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.4e-174], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-117], t$95$1, N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.7999999999999999e41

   1. Initial program 92.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 82.7%

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

   if -2.7999999999999999e41 < a < -8.20000000000000029e-24 or -3.4000000000000002e-174 < a < 3.19999999999999995e-117

   1. Initial program 94.1%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

      1. clear-num 97.5%

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

      2. associate-/r/ 97.7%

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

      3. clear-num 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in a around 0 92.7%

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

   8. Taylor expanded in z around 0 92.7%

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

      1. neg-mul-1 92.7%

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

      2. sub-neg 92.7%

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

   10. Simplified 92.7%

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

   if -8.20000000000000029e-24 < a < -3.7000000000000003e-58

   1. Initial program 99.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.2%

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

      3. clear-num 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in t around inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. associate-*r* 99.6%

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

      3. neg-mul-1 99.6%

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

   9. Simplified 99.6%

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

       1. div-inv 99.2%

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

       2. add-sqr-sqrt 73.6%

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

       3. sqrt-unprod 74.7%

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

       4. sqr-neg 74.7%

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

       5. sqrt-unprod 0.1%

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

       6. add-sqr-sqrt 0.7%

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

       7. distribute-lft-neg-in 0.7%

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

       8. cancel-sign-sub-inv 0.7%

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

       9. div-inv 0.7%

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

       10. associate-/l* 0.7%

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

       11. add-sqr-sqrt 0.1%

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

       12. sqrt-unprod 74.7%

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

       13. sqr-neg 74.7%

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

       14. sqrt-unprod 73.6%

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

       15. add-sqr-sqrt 99.6%

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

   11. Applied egg-rr 99.6%

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

   12. Taylor expanded in x around 0 99.6%

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

       1. mul-1-neg 99.6%

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

       2. associate-*r/ 99.6%

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

       3. *-commutative 99.6%

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

       4. distribute-rgt-neg-in 99.6%

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

   14. Simplified 99.6%

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

   if -3.7000000000000003e-58 < a < -3.4000000000000002e-174

   1. Initial program 79.1%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-*l/ 97.2%

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

      3. *-commutative 97.2%

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

   7. Simplified 97.2%

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

   if 3.19999999999999995e-117 < a

   1. Initial program 90.7%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. associate-/l* 80.7%

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

   7. Simplified 80.7%

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

      1. associate-/r/ 82.0%

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

   9. Applied egg-rr 82.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{-y}{z - a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-174}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-181}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-121}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.45e-73)
   (+ x (/ y (/ a t)))
   (if (<= a -1.3e-181)
     (+ x y)
     (if (<= a 2e-121) (- x (* y (/ t z))) (+ x (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e-73) {
		tmp = x + (y / (a / t));
	} else if (a <= -1.3e-181) {
		tmp = x + y;
	} else if (a <= 2e-121) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.45d-73)) then
        tmp = x + (y / (a / t))
    else if (a <= (-1.3d-181)) then
        tmp = x + y
    else if (a <= 2d-121) then
        tmp = x - (y * (t / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e-73) {
		tmp = x + (y / (a / t));
	} else if (a <= -1.3e-181) {
		tmp = x + y;
	} else if (a <= 2e-121) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.45e-73:
		tmp = x + (y / (a / t))
	elif a <= -1.3e-181:
		tmp = x + y
	elif a <= 2e-121:
		tmp = x - (y * (t / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.45e-73)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (a <= -1.3e-181)
		tmp = Float64(x + y);
	elseif (a <= 2e-121)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.45e-73)
		tmp = x + (y / (a / t));
	elseif (a <= -1.3e-181)
		tmp = x + y;
	elseif (a <= 2e-121)
		tmp = x - (y * (t / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.45e-73], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e-181], N[(x + y), $MachinePrecision], If[LessEqual[a, 2e-121], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.45000000000000014e-73

   1. Initial program 90.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 77.2%

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

   if -2.45000000000000014e-73 < a < -1.29999999999999999e-181

   1. Initial program 83.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 92.4%

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

      1. +-commutative 92.4%

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

   7. Simplified 92.4%

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

   if -1.29999999999999999e-181 < a < 2e-121

   1. Initial program 97.0%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

      1. clear-num 97.0%

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

      2. associate-/r/ 97.1%

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

      3. clear-num 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in t around inf 79.1%

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

      1. associate-*r/ 79.1%

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

      2. associate-*r* 79.1%

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

      3. neg-mul-1 79.1%

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

   9. Simplified 79.1%

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

   10. Taylor expanded in z around inf 74.6%

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

       1. mul-1-neg 74.6%

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

       2. unsub-neg 74.6%

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

       3. associate-/l* 72.0%

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

   12. Simplified 72.0%

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

       1. associate-/r/ 74.6%

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

   14. Applied egg-rr 74.6%

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

   if 2e-121 < a

   1. Initial program 90.7%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. associate-/l* 80.7%

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

   7. Simplified 80.7%

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

      1. associate-/r/ 82.0%

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

   9. Applied egg-rr 82.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-181}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-121}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-117}:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.55e-65)
   (+ x (/ y (/ a t)))
   (if (<= a -2.2e-185)
     (+ x y)
     (if (<= a 1.12e-117) (- x (/ (* t y) z)) (+ x (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.55e-65) {
		tmp = x + (y / (a / t));
	} else if (a <= -2.2e-185) {
		tmp = x + y;
	} else if (a <= 1.12e-117) {
		tmp = x - ((t * y) / z);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.55d-65)) then
        tmp = x + (y / (a / t))
    else if (a <= (-2.2d-185)) then
        tmp = x + y
    else if (a <= 1.12d-117) then
        tmp = x - ((t * y) / z)
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.55e-65) {
		tmp = x + (y / (a / t));
	} else if (a <= -2.2e-185) {
		tmp = x + y;
	} else if (a <= 1.12e-117) {
		tmp = x - ((t * y) / z);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.55e-65:
		tmp = x + (y / (a / t))
	elif a <= -2.2e-185:
		tmp = x + y
	elif a <= 1.12e-117:
		tmp = x - ((t * y) / z)
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.55e-65)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (a <= -2.2e-185)
		tmp = Float64(x + y);
	elseif (a <= 1.12e-117)
		tmp = Float64(x - Float64(Float64(t * y) / z));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.55e-65)
		tmp = x + (y / (a / t));
	elseif (a <= -2.2e-185)
		tmp = x + y;
	elseif (a <= 1.12e-117)
		tmp = x - ((t * y) / z);
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.55e-65], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.2e-185], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.12e-117], N[(x - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.55e-65

   1. Initial program 90.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 77.2%

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

   if -2.55e-65 < a < -2.2e-185

   1. Initial program 83.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 92.4%

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

      1. +-commutative 92.4%

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

   7. Simplified 92.4%

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

   if -2.2e-185 < a < 1.12e-117

   1. Initial program 97.0%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

      1. clear-num 97.0%

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

      2. associate-/r/ 97.1%

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

      3. clear-num 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in t around inf 79.1%

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

      1. associate-*r/ 79.1%

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

      2. associate-*r* 79.1%

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

      3. neg-mul-1 79.1%

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

   9. Simplified 79.1%

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

       1. div-inv 79.0%

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

       2. add-sqr-sqrt 47.8%

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

       3. sqrt-unprod 48.8%

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

       4. sqr-neg 48.8%

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

       5. sqrt-unprod 10.5%

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

       6. add-sqr-sqrt 33.0%

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

       7. distribute-lft-neg-in 33.0%

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

       8. cancel-sign-sub-inv 33.0%

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

       9. div-inv 33.0%

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

       10. associate-/l* 31.6%

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

       11. add-sqr-sqrt 10.5%

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

       12. sqrt-unprod 46.4%

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

       13. sqr-neg 46.4%

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

       14. sqrt-unprod 43.9%

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

       15. add-sqr-sqrt 74.9%

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

   11. Applied egg-rr 74.9%

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

   12. Taylor expanded in z around inf 74.6%

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

   if 1.12e-117 < a

   1. Initial program 90.7%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. associate-/l* 80.7%

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

   7. Simplified 80.7%

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

      1. associate-/r/ 82.0%

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

   9. Applied egg-rr 82.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-117}:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+173}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-185} \lor \neg \left(a \leq 2.9 \cdot 10^{-174}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+173)
   x
   (if (or (<= a 2.4e-185) (not (<= a 2.9e-174))) (+ x y) (* t (/ (- y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+173) {
		tmp = x;
	} else if ((a <= 2.4e-185) || !(a <= 2.9e-174)) {
		tmp = x + y;
	} else {
		tmp = t * (-y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.05d+173)) then
        tmp = x
    else if ((a <= 2.4d-185) .or. (.not. (a <= 2.9d-174))) then
        tmp = x + y
    else
        tmp = t * (-y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+173) {
		tmp = x;
	} else if ((a <= 2.4e-185) || !(a <= 2.9e-174)) {
		tmp = x + y;
	} else {
		tmp = t * (-y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e+173:
		tmp = x
	elif (a <= 2.4e-185) or not (a <= 2.9e-174):
		tmp = x + y
	else:
		tmp = t * (-y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+173)
		tmp = x;
	elseif ((a <= 2.4e-185) || !(a <= 2.9e-174))
		tmp = Float64(x + y);
	else
		tmp = Float64(t * Float64(Float64(-y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.05e+173)
		tmp = x;
	elseif ((a <= 2.4e-185) || ~((a <= 2.9e-174)))
		tmp = x + y;
	else
		tmp = t * (-y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+173], x, If[Or[LessEqual[a, 2.4e-185], N[Not[LessEqual[a, 2.9e-174]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.04999999999999988e173

   1. Initial program 92.7%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around inf 73.8%

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

   if -2.04999999999999988e173 < a < 2.4000000000000001e-185 or 2.9000000000000001e-174 < a

   1. Initial program 91.5%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 63.4%

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

      1. +-commutative 63.4%

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

   7. Simplified 63.4%

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

   if 2.4000000000000001e-185 < a < 2.9000000000000001e-174

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.7%

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

      3. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

      3. neg-mul-1 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in z around inf 99.7%

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

       1. mul-1-neg 99.7%

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

       2. unsub-neg 99.7%

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

       3. associate-/l* 100.0%

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

   12. Simplified 100.0%

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

   13. Taylor expanded in x around 0 99.7%

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

       1. associate-*r/ 100.0%

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

       2. neg-mul-1 100.0%

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

       3. distribute-rgt-neg-in 100.0%

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

       4. distribute-neg-frac 100.0%

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

   15. Simplified 100.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+173}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-185} \lor \neg \left(a \leq 2.9 \cdot 10^{-174}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-15} \lor \neg \left(t \leq 1.15 \cdot 10^{-59}\right):\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.2e-15) (not (<= t 1.15e-59)))
   (- x (/ t (/ (- z a) y)))
   (+ x (* z (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e-15) || !(t <= 1.15e-59)) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.2d-15)) .or. (.not. (t <= 1.15d-59))) then
        tmp = x - (t / ((z - a) / y))
    else
        tmp = x + (z * (y / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e-15) || !(t <= 1.15e-59)) {
		tmp = x - (t / ((z - a) / y));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.2e-15) or not (t <= 1.15e-59):
		tmp = x - (t / ((z - a) / y))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.2e-15) || !(t <= 1.15e-59))
		tmp = Float64(x - Float64(t / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.2e-15) || ~((t <= 1.15e-59)))
		tmp = x - (t / ((z - a) / y));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.2e-15], N[Not[LessEqual[t, 1.15e-59]], $MachinePrecision]], N[(x - N[(t / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.19999999999999986e-15 or 1.1499999999999999e-59 < t

   1. Initial program 89.5%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

      1. clear-num 98.4%

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

      2. associate-/r/ 98.5%

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

      3. clear-num 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in t around inf 85.0%

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

      1. associate-*r/ 85.0%

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

      2. associate-*r* 85.0%

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

      3. neg-mul-1 85.0%

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

   9. Simplified 85.0%

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

       1. div-inv 85.0%

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

       2. add-sqr-sqrt 47.7%

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

       3. sqrt-unprod 45.2%

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

       4. sqr-neg 45.2%

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

       5. sqrt-unprod 16.0%

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

       6. add-sqr-sqrt 40.2%

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

       7. distribute-lft-neg-in 40.2%

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

       8. cancel-sign-sub-inv 40.2%

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

       9. div-inv 40.2%

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

       10. associate-/l* 41.9%

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

       11. add-sqr-sqrt 16.2%

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

       12. sqrt-unprod 46.2%

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

       13. sqr-neg 46.2%

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

       14. sqrt-unprod 50.5%

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

       15. add-sqr-sqrt 89.1%

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

   11. Applied egg-rr 89.1%

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

   if -2.19999999999999986e-15 < t < 1.1499999999999999e-59

   1. Initial program 94.4%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around 0 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-*l/ 91.7%

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

      3. *-commutative 91.7%

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

   7. Simplified 91.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-15} \lor \neg \left(t \leq 1.15 \cdot 10^{-59}\right):\\ \;\;\;\;x - \frac{t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{+111} \lor \neg \left(z \leq 2.05 \cdot 10^{+91}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.32e+111) (not (<= z 2.05e+91))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.32e+111) || !(z <= 2.05e+91)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.32d+111)) .or. (.not. (z <= 2.05d+91))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.32e+111) || !(z <= 2.05e+91)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.32e+111) or not (z <= 2.05e+91):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.32e+111) || !(z <= 2.05e+91))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.32e+111) || ~((z <= 2.05e+91)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.32e+111], N[Not[LessEqual[z, 2.05e+91]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.32e111 or 2.0500000000000001e91 < z

   1. Initial program 82.4%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in z around inf 82.7%

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

      1. +-commutative 82.7%

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

   7. Simplified 82.7%

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

   if -2.32e111 < z < 2.0500000000000001e91

   1. Initial program 96.5%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 73.3%

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

      1. associate-/r/ 70.4%

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

   7. Applied egg-rr 70.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{+111} \lor \neg \left(z \leq 2.05 \cdot 10^{+91}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{+111} \lor \neg \left(z \leq 2.05 \cdot 10^{+91}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.32e+111) (not (<= z 2.05e+91))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.32e+111) || !(z <= 2.05e+91)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.32d+111)) .or. (.not. (z <= 2.05d+91))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.32e+111) || !(z <= 2.05e+91)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.32e+111) or not (z <= 2.05e+91):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.32e+111) || !(z <= 2.05e+91))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.32e+111) || ~((z <= 2.05e+91)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.32e+111], N[Not[LessEqual[z, 2.05e+91]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.32e111 or 2.0500000000000001e91 < z

   1. Initial program 82.4%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in z around inf 82.7%

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

      1. +-commutative 82.7%

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

   7. Simplified 82.7%

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

   if -2.32e111 < z < 2.0500000000000001e91

   1. Initial program 96.5%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 73.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{+111} \lor \neg \left(z \leq 2.05 \cdot 10^{+91}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-*l/ 94.8%

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

3. Simplified 94.8%

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

5. Final simplification 94.8%

   \[\leadsto x + \left(z - t\right) \cdot \frac{y}{z - a} \]
6. Add Preprocessing

Alternative 11: 62.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -3.5e+174) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+174) {
		tmp = x;
	} 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 <= (-3.5d+174)) then
        tmp = x
    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 <= -3.5e+174) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+174:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+174)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+174)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+174], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5000000000000001e174

   1. Initial program 92.7%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around inf 73.8%

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

   if -3.5000000000000001e174 < a

   1. Initial program 91.7%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in z around inf 62.0%

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

      1. +-commutative 62.0%

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

   7. Simplified 62.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.2% accurate, 11.0× 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 91.8%

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

   1. associate-*l/ 94.8%

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

3. Simplified 94.8%

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

5. Taylor expanded in x around inf 54.6%

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

6. Final simplification 54.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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