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

Percentage Accurate: 85.3% → 98.3%

Time: 9.2s

Alternatives: 14

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: 85.3% 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: 98.3% 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]

Derivation

1. Initial program 86.4%

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

   1. associate-/l* 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 78.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+87}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- z a))))))
   (if (<= z -1.35e-153)
     t_1
     (if (<= z 2.4e-64)
       (+ x (/ t (/ a y)))
       (if (<= z 8.5e-12)
         t_1
         (if (<= z 2.35e+23)
           (+ x (/ y (/ a t)))
           (if (<= z 2.3e+87) (- x (* y (/ t z))) (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double tmp;
	if (z <= -1.35e-153) {
		tmp = t_1;
	} else if (z <= 2.4e-64) {
		tmp = x + (t / (a / y));
	} else if (z <= 8.5e-12) {
		tmp = t_1;
	} else if (z <= 2.35e+23) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.3e+87) {
		tmp = x - (y * (t / z));
	} 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 + (z * (y / (z - a)))
    if (z <= (-1.35d-153)) then
        tmp = t_1
    else if (z <= 2.4d-64) then
        tmp = x + (t / (a / y))
    else if (z <= 8.5d-12) then
        tmp = t_1
    else if (z <= 2.35d+23) then
        tmp = x + (y / (a / t))
    else if (z <= 2.3d+87) then
        tmp = x - (y * (t / z))
    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 * (y / (z - a)));
	double tmp;
	if (z <= -1.35e-153) {
		tmp = t_1;
	} else if (z <= 2.4e-64) {
		tmp = x + (t / (a / y));
	} else if (z <= 8.5e-12) {
		tmp = t_1;
	} else if (z <= 2.35e+23) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.3e+87) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (z - a)))
	tmp = 0
	if z <= -1.35e-153:
		tmp = t_1
	elif z <= 2.4e-64:
		tmp = x + (t / (a / y))
	elif z <= 8.5e-12:
		tmp = t_1
	elif z <= 2.35e+23:
		tmp = x + (y / (a / t))
	elif z <= 2.3e+87:
		tmp = x - (y * (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(z - a))))
	tmp = 0.0
	if (z <= -1.35e-153)
		tmp = t_1;
	elseif (z <= 2.4e-64)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 8.5e-12)
		tmp = t_1;
	elseif (z <= 2.35e+23)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 2.3e+87)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (z - a)));
	tmp = 0.0;
	if (z <= -1.35e-153)
		tmp = t_1;
	elseif (z <= 2.4e-64)
		tmp = x + (t / (a / y));
	elseif (z <= 8.5e-12)
		tmp = t_1;
	elseif (z <= 2.35e+23)
		tmp = x + (y / (a / t));
	elseif (z <= 2.3e+87)
		tmp = x - (y * (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e-153], t$95$1, If[LessEqual[z, 2.4e-64], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-12], t$95$1, If[LessEqual[z, 2.35e+23], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+87], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.35000000000000005e-153 or 2.39999999999999998e-64 < z < 8.4999999999999997e-12

   1. Initial program 88.4%

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

      1. associate-/l* 88.4%

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

      2. clear-num 88.4%

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

      3. associate-/r/ 88.4%

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

   5. Applied egg-rr 88.4%

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

   6. Taylor expanded in t around 0 75.0%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   if -1.35000000000000005e-153 < z < 2.39999999999999998e-64

   1. Initial program 95.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. Taylor expanded in z around 0 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-/l* 90.8%

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

      3. associate-/r/ 88.7%

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

   6. Applied egg-rr 88.7%

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

      1. associate-*l/ 86.4%

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

      2. associate-/l* 90.8%

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

   8. Applied egg-rr 90.8%

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

   if 8.4999999999999997e-12 < z < 2.3499999999999999e23

   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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if 2.3499999999999999e23 < z < 2.3000000000000002e87

   1. Initial program 92.9%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around 0 92.3%

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

      1. *-commutative 92.3%

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

      2. associate-/l* 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in z around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*r/ 84.3%

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

      4. distribute-rgt-neg-in 84.3%

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

   9. Simplified 84.3%

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

   10. Taylor expanded in x around 0 84.4%

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

       1. +-commutative 84.4%

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

       2. mul-1-neg 84.4%

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

       3. unsub-neg 84.4%

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

       4. *-commutative 84.4%

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

       5. associate-*l/ 84.4%

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

       6. *-commutative 84.4%

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

   12. Simplified 84.4%

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

   if 2.3000000000000002e87 < z

   1. Initial program 63.2%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 90.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-153}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+87}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 79.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- z a))))))
   (if (<= z -2.9e-153)
     t_1
     (if (<= z 9e-69)
       (+ x (/ t (/ a y)))
       (if (<= z 9.5e-12)
         t_1
         (if (<= z 9.2e+22) (+ x (/ y (/ a t))) (+ x (* (- z t) (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double tmp;
	if (z <= -2.9e-153) {
		tmp = t_1;
	} else if (z <= 9e-69) {
		tmp = x + (t / (a / y));
	} else if (z <= 9.5e-12) {
		tmp = t_1;
	} else if (z <= 9.2e+22) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + ((z - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / (z - a)))
    if (z <= (-2.9d-153)) then
        tmp = t_1
    else if (z <= 9d-69) then
        tmp = x + (t / (a / y))
    else if (z <= 9.5d-12) then
        tmp = t_1
    else if (z <= 9.2d+22) then
        tmp = x + (y / (a / t))
    else
        tmp = x + ((z - 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 t_1 = x + (z * (y / (z - a)));
	double tmp;
	if (z <= -2.9e-153) {
		tmp = t_1;
	} else if (z <= 9e-69) {
		tmp = x + (t / (a / y));
	} else if (z <= 9.5e-12) {
		tmp = t_1;
	} else if (z <= 9.2e+22) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + ((z - t) * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (z - a)))
	tmp = 0
	if z <= -2.9e-153:
		tmp = t_1
	elif z <= 9e-69:
		tmp = x + (t / (a / y))
	elif z <= 9.5e-12:
		tmp = t_1
	elif z <= 9.2e+22:
		tmp = x + (y / (a / t))
	else:
		tmp = x + ((z - t) * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(z - a))))
	tmp = 0.0
	if (z <= -2.9e-153)
		tmp = t_1;
	elseif (z <= 9e-69)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 9.5e-12)
		tmp = t_1;
	elseif (z <= 9.2e+22)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (z - a)));
	tmp = 0.0;
	if (z <= -2.9e-153)
		tmp = t_1;
	elseif (z <= 9e-69)
		tmp = x + (t / (a / y));
	elseif (z <= 9.5e-12)
		tmp = t_1;
	elseif (z <= 9.2e+22)
		tmp = x + (y / (a / t));
	else
		tmp = x + ((z - t) * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-153], t$95$1, If[LessEqual[z, 9e-69], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-12], t$95$1, If[LessEqual[z, 9.2e+22], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000002e-153 or 9.00000000000000019e-69 < z < 9.4999999999999995e-12

   1. Initial program 88.4%

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

      1. associate-/l* 88.4%

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

      2. clear-num 88.4%

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

      3. associate-/r/ 88.4%

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

   5. Applied egg-rr 88.4%

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

   6. Taylor expanded in t around 0 75.0%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   if -2.90000000000000002e-153 < z < 9.00000000000000019e-69

   1. Initial program 95.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. Taylor expanded in z around 0 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-/l* 90.8%

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

      3. associate-/r/ 88.7%

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

   6. Applied egg-rr 88.7%

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

      1. associate-*l/ 86.4%

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

      2. associate-/l* 90.8%

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

   8. Applied egg-rr 90.8%

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

   if 9.4999999999999995e-12 < z < 9.2000000000000008e22

   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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if 9.2000000000000008e22 < z

   1. Initial program 69.8%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 90.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-153}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 4: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ z (- z t))))))
   (if (<= z -5.8e-111)
     t_1
     (if (<= z 3.5e-67)
       (+ x (/ t (/ a y)))
       (if (<= z 7.2e-13)
         (+ x (* z (/ y (- z a))))
         (if (<= z 9.2e+22) (+ x (/ y (/ a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -5.8e-111) {
		tmp = t_1;
	} else if (z <= 3.5e-67) {
		tmp = x + (t / (a / y));
	} else if (z <= 7.2e-13) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 9.2e+22) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (z / (z - t)))
    if (z <= (-5.8d-111)) then
        tmp = t_1
    else if (z <= 3.5d-67) then
        tmp = x + (t / (a / y))
    else if (z <= 7.2d-13) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= 9.2d+22) then
        tmp = x + (y / (a / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -5.8e-111) {
		tmp = t_1;
	} else if (z <= 3.5e-67) {
		tmp = x + (t / (a / y));
	} else if (z <= 7.2e-13) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= 9.2e+22) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -5.8e-111:
		tmp = t_1
	elif z <= 3.5e-67:
		tmp = x + (t / (a / y))
	elif z <= 7.2e-13:
		tmp = x + (z * (y / (z - a)))
	elif z <= 9.2e+22:
		tmp = x + (y / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -5.8e-111)
		tmp = t_1;
	elseif (z <= 3.5e-67)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 7.2e-13)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= 9.2e+22)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -5.8e-111)
		tmp = t_1;
	elseif (z <= 3.5e-67)
		tmp = x + (t / (a / y));
	elseif (z <= 7.2e-13)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= 9.2e+22)
		tmp = x + (y / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-111], t$95$1, If[LessEqual[z, 3.5e-67], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-13], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+22], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.80000000000000003e-111 or 9.2000000000000008e22 < z

   1. Initial program 80.3%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in a around 0 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-/l* 86.8%

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

   6. Simplified 86.8%

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

   if -5.80000000000000003e-111 < z < 3.5e-67

   1. Initial program 95.5%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-/l* 89.4%

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

      3. associate-/r/ 87.4%

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

   6. Applied egg-rr 87.4%

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

      1. associate-*l/ 85.3%

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

      2. associate-/l* 89.4%

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

   8. Applied egg-rr 89.4%

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

   if 3.5e-67 < z < 7.1999999999999996e-13

   1. Initial program 92.3%

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

      1. associate-/l* 92.3%

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

      2. clear-num 92.2%

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

      3. associate-/r/ 92.3%

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

   5. Applied egg-rr 92.3%

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

   6. Taylor expanded in t around 0 87.8%

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

      1. associate-*l/ 87.8%

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

      2. *-commutative 87.8%

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

   8. Simplified 87.8%

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

   if 7.1999999999999996e-13 < z < 9.2000000000000008e22

   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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 5: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ (- z a) z)))))
   (if (<= z -2.9e-153)
     t_1
     (if (<= z 7.4e-65)
       (+ x (/ t (/ a y)))
       (if (<= z 1.15e-12)
         t_1
         (if (<= z 9.5e+22) (+ x (/ y (/ a t))) (+ x (/ y (/ z (- z t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / ((z - a) / z));
	double tmp;
	if (z <= -2.9e-153) {
		tmp = t_1;
	} else if (z <= 7.4e-65) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.15e-12) {
		tmp = t_1;
	} else if (z <= 9.5e+22) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / ((z - a) / z))
    if (z <= (-2.9d-153)) then
        tmp = t_1
    else if (z <= 7.4d-65) then
        tmp = x + (t / (a / y))
    else if (z <= 1.15d-12) then
        tmp = t_1
    else if (z <= 9.5d+22) then
        tmp = x + (y / (a / t))
    else
        tmp = x + (y / (z / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / ((z - a) / z));
	double tmp;
	if (z <= -2.9e-153) {
		tmp = t_1;
	} else if (z <= 7.4e-65) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.15e-12) {
		tmp = t_1;
	} else if (z <= 9.5e+22) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / ((z - a) / z))
	tmp = 0
	if z <= -2.9e-153:
		tmp = t_1
	elif z <= 7.4e-65:
		tmp = x + (t / (a / y))
	elif z <= 1.15e-12:
		tmp = t_1
	elif z <= 9.5e+22:
		tmp = x + (y / (a / t))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(Float64(z - a) / z)))
	tmp = 0.0
	if (z <= -2.9e-153)
		tmp = t_1;
	elseif (z <= 7.4e-65)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.15e-12)
		tmp = t_1;
	elseif (z <= 9.5e+22)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / ((z - a) / z));
	tmp = 0.0;
	if (z <= -2.9e-153)
		tmp = t_1;
	elseif (z <= 7.4e-65)
		tmp = x + (t / (a / y));
	elseif (z <= 1.15e-12)
		tmp = t_1;
	elseif (z <= 9.5e+22)
		tmp = x + (y / (a / t));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-153], t$95$1, If[LessEqual[z, 7.4e-65], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-12], t$95$1, If[LessEqual[z, 9.5e+22], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000002e-153 or 7.4e-65 < z < 1.14999999999999995e-12

   1. Initial program 88.4%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around 0 75.0%

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

      1. associate-/l* 82.4%

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

   6. Simplified 82.4%

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

   if -2.90000000000000002e-153 < z < 7.4e-65

   1. Initial program 95.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. Taylor expanded in z around 0 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-/l* 90.8%

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

      3. associate-/r/ 88.7%

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

   6. Applied egg-rr 88.7%

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

      1. associate-*l/ 86.4%

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

      2. associate-/l* 90.8%

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

   8. Applied egg-rr 90.8%

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

   if 1.14999999999999995e-12 < z < 9.49999999999999937e22

   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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if 9.49999999999999937e22 < z

   1. Initial program 69.8%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in a around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-/l* 93.9%

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

   6. Simplified 93.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-153}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 6: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot t}{z - a}\\ t_2 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-206}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y t) (- z a)))) (t_2 (+ x (/ y (/ z (- z t))))))
   (if (<= z -5.2e-38)
     t_2
     (if (<= z -8.5e-146)
       t_1
       (if (<= z 4.2e-206)
         (+ x (/ (- t z) (/ a y)))
         (if (<= z 5.8e+24) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * t) / (z - a));
	double t_2 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -5.2e-38) {
		tmp = t_2;
	} else if (z <= -8.5e-146) {
		tmp = t_1;
	} else if (z <= 4.2e-206) {
		tmp = x + ((t - z) / (a / y));
	} else if (z <= 5.8e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((y * t) / (z - a))
    t_2 = x + (y / (z / (z - t)))
    if (z <= (-5.2d-38)) then
        tmp = t_2
    else if (z <= (-8.5d-146)) then
        tmp = t_1
    else if (z <= 4.2d-206) then
        tmp = x + ((t - z) / (a / y))
    else if (z <= 5.8d+24) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * t) / (z - a));
	double t_2 = x + (y / (z / (z - t)));
	double tmp;
	if (z <= -5.2e-38) {
		tmp = t_2;
	} else if (z <= -8.5e-146) {
		tmp = t_1;
	} else if (z <= 4.2e-206) {
		tmp = x + ((t - z) / (a / y));
	} else if (z <= 5.8e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * t) / (z - a))
	t_2 = x + (y / (z / (z - t)))
	tmp = 0
	if z <= -5.2e-38:
		tmp = t_2
	elif z <= -8.5e-146:
		tmp = t_1
	elif z <= 4.2e-206:
		tmp = x + ((t - z) / (a / y))
	elif z <= 5.8e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * t) / Float64(z - a)))
	t_2 = Float64(x + Float64(y / Float64(z / Float64(z - t))))
	tmp = 0.0
	if (z <= -5.2e-38)
		tmp = t_2;
	elseif (z <= -8.5e-146)
		tmp = t_1;
	elseif (z <= 4.2e-206)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	elseif (z <= 5.8e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * t) / (z - a));
	t_2 = x + (y / (z / (z - t)));
	tmp = 0.0;
	if (z <= -5.2e-38)
		tmp = t_2;
	elseif (z <= -8.5e-146)
		tmp = t_1;
	elseif (z <= 4.2e-206)
		tmp = x + ((t - z) / (a / y));
	elseif (z <= 5.8e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-38], t$95$2, If[LessEqual[z, -8.5e-146], t$95$1, If[LessEqual[z, 4.2e-206], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000022e-38 or 5.79999999999999958e24 < z

   1. Initial program 77.9%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around 0 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-/l* 90.8%

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

   6. Simplified 90.8%

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

   if -5.20000000000000022e-38 < z < -8.4999999999999997e-146 or 4.2000000000000002e-206 < z < 5.79999999999999958e24

   1. Initial program 98.6%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around inf 88.9%

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

      1. associate-*r/ 88.9%

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

      2. mul-1-neg 88.9%

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

      3. distribute-rgt-neg-out 88.9%

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

   6. Simplified 88.9%

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

   if -8.4999999999999997e-146 < z < 4.2000000000000002e-206

   1. Initial program 92.7%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in a around inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. *-commutative 91.0%

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

      3. associate-/l* 97.6%

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

   6. Simplified 97.6%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-146}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-206}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 7: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-138}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e-80)
   (+ x y)
   (if (<= z -6.5e-138)
     (- x (/ y (/ a t)))
     (if (<= z 6e+24) (+ x (/ t (/ a y))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e-80) {
		tmp = x + y;
	} else if (z <= -6.5e-138) {
		tmp = x - (y / (a / t));
	} else if (z <= 6e+24) {
		tmp = x + (t / (a / 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) :: tmp
    if (z <= (-2.7d-80)) then
        tmp = x + y
    else if (z <= (-6.5d-138)) then
        tmp = x - (y / (a / t))
    else if (z <= 6d+24) then
        tmp = x + (t / (a / 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 tmp;
	if (z <= -2.7e-80) {
		tmp = x + y;
	} else if (z <= -6.5e-138) {
		tmp = x - (y / (a / t));
	} else if (z <= 6e+24) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e-80:
		tmp = x + y
	elif z <= -6.5e-138:
		tmp = x - (y / (a / t))
	elif z <= 6e+24:
		tmp = x + (t / (a / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e-80)
		tmp = Float64(x + y);
	elseif (z <= -6.5e-138)
		tmp = Float64(x - Float64(y / Float64(a / t)));
	elseif (z <= 6e+24)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e-80)
		tmp = x + y;
	elseif (z <= -6.5e-138)
		tmp = x - (y / (a / t));
	elseif (z <= 6e+24)
		tmp = x + (t / (a / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e-80], N[(x + y), $MachinePrecision], If[LessEqual[z, -6.5e-138], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+24], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000002e-80 or 5.9999999999999999e24 < z

   1. Initial program 79.0%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 80.3%

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

   if -2.7000000000000002e-80 < z < -6.4999999999999999e-138

   1. Initial program 99.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around 0 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-/l* 51.7%

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

      3. associate-/r/ 54.0%

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

   6. Applied egg-rr 54.0%

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

      1. frac-2neg 54.0%

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

      2. distribute-frac-neg 54.0%

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

      3. add-sqr-sqrt 27.3%

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

      4. sqrt-unprod 48.3%

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

      5. sqr-neg 48.3%

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

      6. sqrt-unprod 38.1%

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

      7. add-sqr-sqrt 79.1%

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

      8. frac-2neg 79.1%

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

      9. cancel-sign-sub-inv 79.1%

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

      10. *-commutative 79.1%

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

      11. clear-num 79.1%

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

      12. div-inv 79.1%

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

   8. Applied egg-rr 79.1%

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

   if -6.4999999999999999e-138 < z < 5.9999999999999999e24

   1. Initial program 95.1%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 86.1%

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

      3. associate-/r/ 84.4%

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

   6. Applied egg-rr 84.4%

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

      1. associate-*l/ 81.6%

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

      2. associate-/l* 86.1%

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

   8. Applied egg-rr 86.1%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-138}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-99} \lor \neg \left(z \leq 1.6 \cdot 10^{+23}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e-99) (not (<= z 1.6e+23)))
   (+ x (/ y (/ z (- z t))))
   (+ x (/ (- t z) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e-99) || !(z <= 1.6e+23)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + ((t - z) / (a / 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 ((z <= (-1.45d-99)) .or. (.not. (z <= 1.6d+23))) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x + ((t - z) / (a / 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 ((z <= -1.45e-99) || !(z <= 1.6e+23)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e-99) or not (z <= 1.6e+23):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x + ((t - z) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e-99) || !(z <= 1.6e+23))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e-99) || ~((z <= 1.6e+23)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x + ((t - z) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e-99], N[Not[LessEqual[z, 1.6e+23]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.44999999999999993e-99 or 1.6e23 < z

   1. Initial program 79.8%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in a around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   if -1.44999999999999993e-99 < z < 1.6e23

   1. Initial program 95.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. Taylor expanded in a around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-/l* 89.4%

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

   6. Simplified 89.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-99} \lor \neg \left(z \leq 1.6 \cdot 10^{+23}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-38} \lor \neg \left(z \leq 1.6 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e-38) (not (<= z 1.6e+23))) (+ x y) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e-38) || !(z <= 1.6e+23)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / 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 ((z <= (-1.75d-38)) .or. (.not. (z <= 1.6d+23))) then
        tmp = x + y
    else
        tmp = x + (t / (a / 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 ((z <= -1.75e-38) || !(z <= 1.6e+23)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e-38) or not (z <= 1.6e+23):
		tmp = x + y
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e-38) || !(z <= 1.6e+23))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.75e-38) || ~((z <= 1.6e+23)))
		tmp = x + y;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e-38], N[Not[LessEqual[z, 1.6e+23]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e-38 or 1.6e23 < z

   1. Initial program 77.9%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 81.4%

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

   if -1.7500000000000001e-38 < z < 1.6e23

   1. Initial program 96.0%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 76.8%

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

      1. *-commutative 76.8%

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

      2. associate-/l* 80.2%

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

      3. associate-/r/ 79.1%

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

   6. Applied egg-rr 79.1%

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

      1. associate-*l/ 76.8%

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

      2. associate-/l* 80.2%

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

   8. Applied egg-rr 80.2%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-38} \lor \neg \left(z \leq 1.6 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e-38) (+ x y) (if (<= z 2.05e+24) (+ x (* y (/ t a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e-38) {
		tmp = x + y;
	} else if (z <= 2.05e+24) {
		tmp = x + (y * (t / a));
	} 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 (z <= (-5.8d-38)) then
        tmp = x + y
    else if (z <= 2.05d+24) then
        tmp = x + (y * (t / a))
    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 (z <= -5.8e-38) {
		tmp = x + y;
	} else if (z <= 2.05e+24) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.8e-38:
		tmp = x + y
	elif z <= 2.05e+24:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e-38)
		tmp = Float64(x + y);
	elseif (z <= 2.05e+24)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.8e-38)
		tmp = x + y;
	elseif (z <= 2.05e+24)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e-38], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.05e+24], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999988e-38 or 2.05e24 < z

   1. Initial program 77.9%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 81.4%

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

   if -5.79999999999999988e-38 < z < 2.05e24

   1. Initial program 96.0%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 76.8%

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

      1. *-commutative 76.8%

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

      2. associate-/l* 80.2%

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

      3. associate-/r/ 79.1%

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

   6. Applied egg-rr 79.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-39}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.46e-39) (+ x y) (if (<= z 4.1e+23) (+ x (* t (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.46e-39) {
		tmp = x + y;
	} else if (z <= 4.1e+23) {
		tmp = x + (t * (y / a));
	} 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 (z <= (-1.46d-39)) then
        tmp = x + y
    else if (z <= 4.1d+23) then
        tmp = x + (t * (y / a))
    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 (z <= -1.46e-39) {
		tmp = x + y;
	} else if (z <= 4.1e+23) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.46e-39:
		tmp = x + y
	elif z <= 4.1e+23:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.46e-39)
		tmp = Float64(x + y);
	elseif (z <= 4.1e+23)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.46e-39)
		tmp = x + y;
	elseif (z <= 4.1e+23)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.46e-39], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.1e+23], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.46000000000000001e-39 or 4.09999999999999996e23 < z

   1. Initial program 77.9%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 81.4%

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

   if -1.46000000000000001e-39 < z < 4.09999999999999996e23

   1. Initial program 96.0%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 76.8%

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

      1. associate-/l* 80.0%

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

      2. associate-/r/ 79.6%

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

   6. Applied egg-rr 79.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-39}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 95.9% 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 86.4%

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

   1. associate-*l/ 97.8%

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

3. Simplified 97.8%

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

4. Final simplification 97.8%

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

Alternative 13: 64.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{-40}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.9e-40) (+ x y) (if (<= z 1.85e+26) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.9e-40) {
		tmp = x + y;
	} else if (z <= 1.85e+26) {
		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 (z <= (-6.9d-40)) then
        tmp = x + y
    else if (z <= 1.85d+26) 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 (z <= -6.9e-40) {
		tmp = x + y;
	} else if (z <= 1.85e+26) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.9e-40:
		tmp = x + y
	elif z <= 1.85e+26:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.9e-40)
		tmp = Float64(x + y);
	elseif (z <= 1.85e+26)
		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 (z <= -6.9e-40)
		tmp = x + y;
	elseif (z <= 1.85e+26)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.9e-40], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.85e+26], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8999999999999996e-40 or 1.84999999999999994e26 < z

   1. Initial program 77.7%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 82.0%

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

   if -6.8999999999999996e-40 < z < 1.84999999999999994e26

   1. Initial program 96.0%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 76.2%

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

   5. Taylor expanded in x around inf 44.0%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{-40}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14: 50.7% 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 86.4%

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

   1. associate-*l/ 97.8%

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

3. Simplified 97.8%

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

4. Taylor expanded in z around 0 60.2%

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

5. Taylor expanded in x around inf 50.6%

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

6. Final simplification 50.6%

   \[\leadsto x \]

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 2023185 
(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))))