Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F

Percentage Accurate: 93.3% → 97.4%

Time: 13.0s

Alternatives: 15

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

5. Taylor expanded in y around 0 91.2%

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

   1. *-commutative 91.2%

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

   2. associate-/l* 96.9%

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

7. Simplified 96.9%

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

8. Final simplification 96.9%

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

Alternative 2: 68.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{a}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) a))))
   (if (<= y -5.4e-49)
     t_1
     (if (<= y 7.2e-143)
       x
       (if (<= y 6.8e-108) (/ (* z (- y)) a) (if (<= y 2.7e-33) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / a);
	double tmp;
	if (y <= -5.4e-49) {
		tmp = t_1;
	} else if (y <= 7.2e-143) {
		tmp = x;
	} else if (y <= 6.8e-108) {
		tmp = (z * -y) / a;
	} else if (y <= 2.7e-33) {
		tmp = x;
	} 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 = y * ((t - z) / a)
    if (y <= (-5.4d-49)) then
        tmp = t_1
    else if (y <= 7.2d-143) then
        tmp = x
    else if (y <= 6.8d-108) then
        tmp = (z * -y) / a
    else if (y <= 2.7d-33) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / a);
	double tmp;
	if (y <= -5.4e-49) {
		tmp = t_1;
	} else if (y <= 7.2e-143) {
		tmp = x;
	} else if (y <= 6.8e-108) {
		tmp = (z * -y) / a;
	} else if (y <= 2.7e-33) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / a)
	tmp = 0
	if y <= -5.4e-49:
		tmp = t_1
	elif y <= 7.2e-143:
		tmp = x
	elif y <= 6.8e-108:
		tmp = (z * -y) / a
	elif y <= 2.7e-33:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / a))
	tmp = 0.0
	if (y <= -5.4e-49)
		tmp = t_1;
	elseif (y <= 7.2e-143)
		tmp = x;
	elseif (y <= 6.8e-108)
		tmp = Float64(Float64(z * Float64(-y)) / a);
	elseif (y <= 2.7e-33)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / a);
	tmp = 0.0;
	if (y <= -5.4e-49)
		tmp = t_1;
	elseif (y <= 7.2e-143)
		tmp = x;
	elseif (y <= 6.8e-108)
		tmp = (z * -y) / a;
	elseif (y <= 2.7e-33)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e-49], t$95$1, If[LessEqual[y, 7.2e-143], x, If[LessEqual[y, 6.8e-108], N[(N[(z * (-y)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.7e-33], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3999999999999999e-49 or 2.7000000000000001e-33 < y

   1. Initial program 85.1%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in x around 0 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-*r/ 72.4%

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

      3. distribute-rgt-neg-out 72.4%

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

      4. *-rgt-identity 72.4%

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

      5. *-rgt-identity 72.4%

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

      6. distribute-neg-frac 72.4%

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

      7. neg-sub0 72.4%

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

      8. associate--r- 72.4%

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

      9. neg-sub0 72.4%

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

      10. +-commutative 72.4%

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

      11. sub-neg 72.4%

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

   7. Simplified 72.4%

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

   if -5.3999999999999999e-49 < y < 7.1999999999999996e-143 or 6.80000000000000004e-108 < y < 2.7000000000000001e-33

   1. Initial program 98.4%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 69.5%

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

   if 7.1999999999999996e-143 < y < 6.80000000000000004e-108

   1. Initial program 100.0%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. associate-*l/ 75.0%

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

      3. *-commutative 75.0%

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

      4. distribute-rgt-neg-in 75.0%

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

      5. *-lft-identity 75.0%

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

      6. associate-*l/ 75.0%

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

      7. remove-double-neg 75.0%

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

      8. neg-mul-1 75.0%

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

      9. associate-*r* 75.0%

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

      10. *-commutative 75.0%

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

      11. neg-mul-1 75.0%

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

      12. *-commutative 75.0%

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

      13. distribute-neg-frac 75.0%

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

      14. metadata-eval 75.0%

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

      15. metadata-eval 75.0%

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

      16. associate-/r* 75.0%

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

      17. neg-mul-1 75.0%

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

      18. associate-*r/ 75.0%

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

      19. *-rgt-identity 75.0%

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

      20. distribute-frac-neg 75.0%

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

      21. remove-double-neg 75.0%

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

   7. Simplified 75.0%

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

      1. *-commutative 75.0%

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

      2. frac-2neg 75.0%

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

      3. remove-double-neg 75.0%

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

      4. associate-*l/ 75.4%

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

   9. Applied egg-rr 75.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+243}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a z)))))
   (if (<= z -1.15e+55)
     t_1
     (if (<= z 0.68)
       (- x (/ y (/ (- a) t)))
       (if (<= z 5e+216)
         t_1
         (if (<= z 2.75e+243) (/ (* y (- t z)) a) (* z (/ y (- a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / z));
	double tmp;
	if (z <= -1.15e+55) {
		tmp = t_1;
	} else if (z <= 0.68) {
		tmp = x - (y / (-a / t));
	} else if (z <= 5e+216) {
		tmp = t_1;
	} else if (z <= 2.75e+243) {
		tmp = (y * (t - z)) / a;
	} else {
		tmp = z * (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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (a / z))
    if (z <= (-1.15d+55)) then
        tmp = t_1
    else if (z <= 0.68d0) then
        tmp = x - (y / (-a / t))
    else if (z <= 5d+216) then
        tmp = t_1
    else if (z <= 2.75d+243) then
        tmp = (y * (t - z)) / a
    else
        tmp = z * (y / -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 / (a / z));
	double tmp;
	if (z <= -1.15e+55) {
		tmp = t_1;
	} else if (z <= 0.68) {
		tmp = x - (y / (-a / t));
	} else if (z <= 5e+216) {
		tmp = t_1;
	} else if (z <= 2.75e+243) {
		tmp = (y * (t - z)) / a;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / z))
	tmp = 0
	if z <= -1.15e+55:
		tmp = t_1
	elif z <= 0.68:
		tmp = x - (y / (-a / t))
	elif z <= 5e+216:
		tmp = t_1
	elif z <= 2.75e+243:
		tmp = (y * (t - z)) / a
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (z <= -1.15e+55)
		tmp = t_1;
	elseif (z <= 0.68)
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	elseif (z <= 5e+216)
		tmp = t_1;
	elseif (z <= 2.75e+243)
		tmp = Float64(Float64(y * Float64(t - z)) / a);
	else
		tmp = Float64(z * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / z));
	tmp = 0.0;
	if (z <= -1.15e+55)
		tmp = t_1;
	elseif (z <= 0.68)
		tmp = x - (y / (-a / t));
	elseif (z <= 5e+216)
		tmp = t_1;
	elseif (z <= 2.75e+243)
		tmp = (y * (t - z)) / a;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+55], t$95$1, If[LessEqual[z, 0.68], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+216], t$95$1, If[LessEqual[z, 2.75e+243], N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.14999999999999994e55 or 0.680000000000000049 < z < 4.9999999999999998e216

   1. Initial program 85.0%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in z around inf 80.2%

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

   if -1.14999999999999994e55 < z < 0.680000000000000049

   1. Initial program 96.0%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around 0 89.3%

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

      1. associate-*r/ 89.3%

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

      2. neg-mul-1 89.3%

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

   7. Simplified 89.3%

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

   if 4.9999999999999998e216 < z < 2.75000000000000002e243

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. associate-*l/ 85.9%

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

      8. fma-def 85.9%

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

      9. sub-neg 85.9%

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

      10. distribute-neg-in 85.9%

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

      11. remove-double-neg 85.9%

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

      12. +-commutative 85.9%

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

      13. sub-neg 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in y around -inf 99.8%

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

   if 2.75000000000000002e243 < z

   1. Initial program 81.4%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 71.7%

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

      1. mul-1-neg 71.7%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. *-lft-identity 90.0%

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

      6. associate-*l/ 89.9%

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

      7. remove-double-neg 89.9%

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

      8. neg-mul-1 89.9%

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

      9. associate-*r* 89.9%

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

      10. *-commutative 89.9%

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

      11. neg-mul-1 89.9%

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

      12. *-commutative 89.9%

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

      13. distribute-neg-frac 89.9%

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

      14. metadata-eval 89.9%

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

      15. metadata-eval 89.9%

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

      16. associate-/r* 89.9%

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

      17. neg-mul-1 89.9%

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

      18. associate-*r/ 90.0%

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

      19. *-rgt-identity 90.0%

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

      20. distribute-frac-neg 90.0%

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

      21. remove-double-neg 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+216}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+243}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))))
   (if (<= z -1.45e+60)
     t_1
     (if (<= z 1.8e-198)
       x
       (if (<= z 4.9e-161) (* y (/ t a)) (if (<= z 4.6e+119) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (z <= -1.45e+60) {
		tmp = t_1;
	} else if (z <= 1.8e-198) {
		tmp = x;
	} else if (z <= 4.9e-161) {
		tmp = y * (t / a);
	} else if (z <= 4.6e+119) {
		tmp = x;
	} 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 = z * (y / -a)
    if (z <= (-1.45d+60)) then
        tmp = t_1
    else if (z <= 1.8d-198) then
        tmp = x
    else if (z <= 4.9d-161) then
        tmp = y * (t / a)
    else if (z <= 4.6d+119) then
        tmp = x
    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 = z * (y / -a);
	double tmp;
	if (z <= -1.45e+60) {
		tmp = t_1;
	} else if (z <= 1.8e-198) {
		tmp = x;
	} else if (z <= 4.9e-161) {
		tmp = y * (t / a);
	} else if (z <= 4.6e+119) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	tmp = 0
	if z <= -1.45e+60:
		tmp = t_1
	elif z <= 1.8e-198:
		tmp = x
	elif z <= 4.9e-161:
		tmp = y * (t / a)
	elif z <= 4.6e+119:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -1.45e+60)
		tmp = t_1;
	elseif (z <= 1.8e-198)
		tmp = x;
	elseif (z <= 4.9e-161)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 4.6e+119)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	tmp = 0.0;
	if (z <= -1.45e+60)
		tmp = t_1;
	elseif (z <= 1.8e-198)
		tmp = x;
	elseif (z <= 4.9e-161)
		tmp = y * (t / a);
	elseif (z <= 4.6e+119)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+60], t$95$1, If[LessEqual[z, 1.8e-198], x, If[LessEqual[z, 4.9e-161], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+119], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e60 or 4.6000000000000001e119 < z

   1. Initial program 83.0%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in z around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. associate-*l/ 65.1%

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

      3. *-commutative 65.1%

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

      4. distribute-rgt-neg-in 65.1%

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

      5. *-lft-identity 65.1%

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

      6. associate-*l/ 65.0%

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

      7. remove-double-neg 65.0%

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

      8. neg-mul-1 65.0%

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

      9. associate-*r* 65.0%

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

      10. *-commutative 65.0%

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

      11. neg-mul-1 65.0%

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

      12. *-commutative 65.0%

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

      13. distribute-neg-frac 65.0%

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

      14. metadata-eval 65.0%

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

      15. metadata-eval 65.0%

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

      16. associate-/r* 65.0%

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

      17. neg-mul-1 65.0%

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

      18. associate-*r/ 65.1%

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

      19. *-rgt-identity 65.1%

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

      20. distribute-frac-neg 65.1%

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

      21. remove-double-neg 65.1%

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

   7. Simplified 65.1%

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

   if -1.45e60 < z < 1.79999999999999999e-198 or 4.90000000000000035e-161 < z < 4.6000000000000001e119

   1. Initial program 95.6%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   if 1.79999999999999999e-198 < z < 4.90000000000000035e-161

   1. Initial program 99.7%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in t around inf 73.8%

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

      1. associate-*l/ 73.9%

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

      2. *-commutative 73.9%

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

   10. Simplified 73.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+59}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+59)
   (/ (- z) (/ a y))
   (if (<= z 1.25e-197)
     x
     (if (<= z 2.8e-161)
       (* y (/ t a))
       (if (<= z 4.9e+119) x (* z (/ y (- a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+59) {
		tmp = -z / (a / y);
	} else if (z <= 1.25e-197) {
		tmp = x;
	} else if (z <= 2.8e-161) {
		tmp = y * (t / a);
	} else if (z <= 4.9e+119) {
		tmp = x;
	} else {
		tmp = z * (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 <= (-3d+59)) then
        tmp = -z / (a / y)
    else if (z <= 1.25d-197) then
        tmp = x
    else if (z <= 2.8d-161) then
        tmp = y * (t / a)
    else if (z <= 4.9d+119) then
        tmp = x
    else
        tmp = z * (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 <= -3e+59) {
		tmp = -z / (a / y);
	} else if (z <= 1.25e-197) {
		tmp = x;
	} else if (z <= 2.8e-161) {
		tmp = y * (t / a);
	} else if (z <= 4.9e+119) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+59:
		tmp = -z / (a / y)
	elif z <= 1.25e-197:
		tmp = x
	elif z <= 2.8e-161:
		tmp = y * (t / a)
	elif z <= 4.9e+119:
		tmp = x
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+59)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= 1.25e-197)
		tmp = x;
	elseif (z <= 2.8e-161)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 4.9e+119)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+59)
		tmp = -z / (a / y);
	elseif (z <= 1.25e-197)
		tmp = x;
	elseif (z <= 2.8e-161)
		tmp = y * (t / a);
	elseif (z <= 4.9e+119)
		tmp = x;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+59], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-197], x, If[LessEqual[z, 2.8e-161], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+119], x, N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3e59

   1. Initial program 82.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. associate-*l/ 60.9%

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

      3. *-commutative 60.9%

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

      4. distribute-rgt-neg-in 60.9%

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

      5. *-lft-identity 60.9%

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

      6. associate-*l/ 60.9%

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

      7. remove-double-neg 60.9%

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

      8. neg-mul-1 60.9%

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

      9. associate-*r* 60.9%

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

      10. *-commutative 60.9%

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

      11. neg-mul-1 60.9%

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

      12. *-commutative 60.9%

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

      13. distribute-neg-frac 60.9%

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

      14. metadata-eval 60.9%

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

      15. metadata-eval 60.9%

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

      16. associate-/r* 60.9%

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

      17. neg-mul-1 60.9%

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

      18. associate-*r/ 60.9%

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

      19. *-rgt-identity 60.9%

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

      20. distribute-frac-neg 60.9%

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

      21. remove-double-neg 60.9%

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

   7. Simplified 60.9%

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

      1. add-sqr-sqrt 42.3%

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

      2. sqrt-unprod 26.0%

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

      3. sqr-neg 26.0%

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

      4. sqrt-unprod 2.3%

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

      5. add-sqr-sqrt 2.9%

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

      6. clear-num 2.9%

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

      7. div-inv 2.9%

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

      8. frac-2neg 2.9%

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

      9. distribute-frac-neg 2.9%

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

      10. add-sqr-sqrt 0.6%

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

      11. sqrt-unprod 15.5%

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

      12. sqr-neg 15.5%

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

      13. sqrt-unprod 18.4%

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

      14. add-sqr-sqrt 60.9%

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

   9. Applied egg-rr 60.9%

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

   if -3e59 < z < 1.2500000000000001e-197 or 2.79999999999999992e-161 < z < 4.89999999999999996e119

   1. Initial program 95.6%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   if 1.2500000000000001e-197 < z < 2.79999999999999992e-161

   1. Initial program 99.7%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in t around inf 73.8%

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

      1. associate-*l/ 73.9%

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

      2. *-commutative 73.9%

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

   10. Simplified 73.9%

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

   if 4.89999999999999996e119 < z

   1. Initial program 84.2%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-*l/ 74.0%

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

      3. *-commutative 74.0%

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

      4. distribute-rgt-neg-in 74.0%

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

      5. *-lft-identity 74.0%

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

      6. associate-*l/ 73.7%

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

      7. remove-double-neg 73.7%

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

      8. neg-mul-1 73.7%

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

      9. associate-*r* 73.7%

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

      10. *-commutative 73.7%

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

      11. neg-mul-1 73.7%

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

      12. *-commutative 73.7%

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

      13. distribute-neg-frac 73.7%

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

      14. metadata-eval 73.7%

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

      15. metadata-eval 73.7%

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

      16. associate-/r* 73.7%

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

      17. neg-mul-1 73.7%

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

      18. associate-*r/ 74.0%

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

      19. *-rgt-identity 74.0%

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

      20. distribute-frac-neg 74.0%

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

      21. remove-double-neg 74.0%

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

   7. Simplified 74.0%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+59}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+132} \lor \neg \left(z \leq 1.05 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.05e+132) (not (<= z 1.05e+175)))
   (/ (- z) (/ a y))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e+132) || !(z <= 1.05e+175)) {
		tmp = -z / (a / 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 <= (-2.05d+132)) .or. (.not. (z <= 1.05d+175))) then
        tmp = -z / (a / 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 <= -2.05e+132) || !(z <= 1.05e+175)) {
		tmp = -z / (a / y);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.05e+132) or not (z <= 1.05e+175):
		tmp = -z / (a / y)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.05e+132) || !(z <= 1.05e+175))
		tmp = Float64(Float64(-z) / Float64(a / 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 <= -2.05e+132) || ~((z <= 1.05e+175)))
		tmp = -z / (a / y);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.05e+132], N[Not[LessEqual[z, 1.05e+175]], $MachinePrecision]], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.04999999999999996e132 or 1.05e175 < z

   1. Initial program 80.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. associate-*l/ 71.5%

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

      3. *-commutative 71.5%

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

      4. distribute-rgt-neg-in 71.5%

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

      5. *-lft-identity 71.5%

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

      6. associate-*l/ 71.5%

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

      7. remove-double-neg 71.5%

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

      8. neg-mul-1 71.5%

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

      9. associate-*r* 71.5%

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

      10. *-commutative 71.5%

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

      11. neg-mul-1 71.5%

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

      12. *-commutative 71.5%

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

      13. distribute-neg-frac 71.5%

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

      14. metadata-eval 71.5%

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

      15. metadata-eval 71.5%

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

      16. associate-/r* 71.5%

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

      17. neg-mul-1 71.5%

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

      18. associate-*r/ 71.5%

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

      19. *-rgt-identity 71.5%

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

      20. distribute-frac-neg 71.5%

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

      21. remove-double-neg 71.5%

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

   7. Simplified 71.5%

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

      1. add-sqr-sqrt 47.0%

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

      2. sqrt-unprod 25.7%

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

      3. sqr-neg 25.7%

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

      4. sqrt-unprod 2.2%

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

      5. add-sqr-sqrt 2.8%

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

      6. clear-num 2.7%

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

      7. div-inv 2.7%

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

      8. frac-2neg 2.7%

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

      9. distribute-frac-neg 2.7%

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

      10. add-sqr-sqrt 0.6%

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

      11. sqrt-unprod 18.0%

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

      12. sqr-neg 18.0%

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

      13. sqrt-unprod 24.3%

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

      14. add-sqr-sqrt 71.6%

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

   9. Applied egg-rr 71.6%

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

   if -2.04999999999999996e132 < z < 1.05e175

   1. Initial program 94.6%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around 0 81.1%

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

      1. cancel-sign-sub-inv 81.1%

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

      2. metadata-eval 81.1%

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

      3. *-lft-identity 81.1%

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

      4. +-commutative 81.1%

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

      5. associate-*r/ 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+132} \lor \neg \left(z \leq 1.05 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+134} \lor \neg \left(z \leq 1.4 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e+134) (not (<= z 1.4e+172)))
   (/ (- z) (/ a y))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e+134) || !(z <= 1.4e+172)) {
		tmp = -z / (a / 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 <= (-3.4d+134)) .or. (.not. (z <= 1.4d+172))) then
        tmp = -z / (a / 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 <= -3.4e+134) || !(z <= 1.4e+172)) {
		tmp = -z / (a / y);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e+134) or not (z <= 1.4e+172):
		tmp = -z / (a / y)
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e+134) || !(z <= 1.4e+172))
		tmp = Float64(Float64(-z) / Float64(a / 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 <= -3.4e+134) || ~((z <= 1.4e+172)))
		tmp = -z / (a / y);
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.4e+134], N[Not[LessEqual[z, 1.4e+172]], $MachinePrecision]], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000018e134 or 1.4e172 < z

   1. Initial program 80.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. associate-*l/ 71.5%

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

      3. *-commutative 71.5%

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

      4. distribute-rgt-neg-in 71.5%

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

      5. *-lft-identity 71.5%

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

      6. associate-*l/ 71.5%

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

      7. remove-double-neg 71.5%

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

      8. neg-mul-1 71.5%

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

      9. associate-*r* 71.5%

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

      10. *-commutative 71.5%

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

      11. neg-mul-1 71.5%

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

      12. *-commutative 71.5%

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

      13. distribute-neg-frac 71.5%

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

      14. metadata-eval 71.5%

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

      15. metadata-eval 71.5%

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

      16. associate-/r* 71.5%

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

      17. neg-mul-1 71.5%

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

      18. associate-*r/ 71.5%

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

      19. *-rgt-identity 71.5%

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

      20. distribute-frac-neg 71.5%

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

      21. remove-double-neg 71.5%

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

   7. Simplified 71.5%

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

      1. add-sqr-sqrt 47.0%

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

      2. sqrt-unprod 25.7%

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

      3. sqr-neg 25.7%

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

      4. sqrt-unprod 2.2%

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

      5. add-sqr-sqrt 2.8%

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

      6. clear-num 2.7%

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

      7. div-inv 2.7%

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

      8. frac-2neg 2.7%

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

      9. distribute-frac-neg 2.7%

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

      10. add-sqr-sqrt 0.6%

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

      11. sqrt-unprod 18.0%

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

      12. sqr-neg 18.0%

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

      13. sqrt-unprod 24.3%

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

      14. add-sqr-sqrt 71.6%

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

   9. Applied egg-rr 71.6%

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

   if -3.40000000000000018e134 < z < 1.4e172

   1. Initial program 94.6%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around 0 81.1%

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

      1. cancel-sign-sub-inv 81.1%

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

      2. metadata-eval 81.1%

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

      3. *-lft-identity 81.1%

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

      4. +-commutative 81.1%

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

      5. associate-*r/ 83.6%

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

   7. Simplified 83.6%

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

      1. clear-num 34.0%

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

      2. div-inv 34.0%

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

   9. Applied egg-rr 83.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+134} \lor \neg \left(z \leq 1.4 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+176}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e-59)
   (+ x (/ t (/ a y)))
   (if (<= t 9.5e+176) (- x (/ y (/ a z))) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e-59) {
		tmp = x + (t / (a / y));
	} else if (t <= 9.5e+176) {
		tmp = x - (y / (a / z));
	} 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 (t <= (-6.8d-59)) then
        tmp = x + (t / (a / y))
    else if (t <= 9.5d+176) then
        tmp = x - (y / (a / z))
    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 (t <= -6.8e-59) {
		tmp = x + (t / (a / y));
	} else if (t <= 9.5e+176) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e-59:
		tmp = x + (t / (a / y))
	elif t <= 9.5e+176:
		tmp = x - (y / (a / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e-59)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (t <= 9.5e+176)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	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 (t <= -6.8e-59)
		tmp = x + (t / (a / y));
	elseif (t <= 9.5e+176)
		tmp = x - (y / (a / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e-59], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+176], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.80000000000000035e-59

   1. Initial program 90.4%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 75.3%

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

      1. cancel-sign-sub-inv 75.3%

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

      2. metadata-eval 75.3%

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

      3. *-lft-identity 75.3%

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

      4. +-commutative 75.3%

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

      5. associate-*r/ 80.6%

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

   7. Simplified 80.6%

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

      1. clear-num 51.4%

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

      2. div-inv 51.4%

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

   9. Applied egg-rr 80.7%

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

   if -6.80000000000000035e-59 < t < 9.4999999999999995e176

   1. Initial program 92.0%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 81.8%

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

   if 9.4999999999999995e176 < t

   1. Initial program 87.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 83.6%

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

      1. cancel-sign-sub-inv 83.6%

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

      2. metadata-eval 83.6%

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

      3. *-lft-identity 83.6%

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

      4. +-commutative 83.6%

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

      5. associate-*r/ 96.1%

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

   7. Simplified 96.1%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+176}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+69} \lor \neg \left(y \leq 2.2 \cdot 10^{+175}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.5e+69) (not (<= y 2.2e+175))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.5e+69) || !(y <= 2.2e+175)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-8.5d+69)) .or. (.not. (y <= 2.2d+175))) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.5e+69) || !(y <= 2.2e+175)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.5e+69) or not (y <= 2.2e+175):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.5e+69) || !(y <= 2.2e+175))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8.5e+69) || ~((y <= 2.2e+175)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.5e+69], N[Not[LessEqual[y, 2.2e+175]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000002e69 or 2.1999999999999999e175 < y

   1. Initial program 81.4%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf 49.2%

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

      1. associate-*r/ 54.9%

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

   7. Simplified 54.9%

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

   if -8.5000000000000002e69 < y < 2.1999999999999999e175

   1. Initial program 95.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 56.6%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+69} \lor \neg \left(y \leq 2.2 \cdot 10^{+175}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.75e+71) (* t (/ y a)) (if (<= y 3e+175) x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.75e+71) {
		tmp = t * (y / a);
	} else if (y <= 3e+175) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-1.75d+71)) then
        tmp = t * (y / a)
    else if (y <= 3d+175) then
        tmp = x
    else
        tmp = 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 (y <= -1.75e+71) {
		tmp = t * (y / a);
	} else if (y <= 3e+175) {
		tmp = x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.75e+71:
		tmp = t * (y / a)
	elif y <= 3e+175:
		tmp = x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.75e+71)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 3e+175)
		tmp = x;
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.75e+71)
		tmp = t * (y / a);
	elseif (y <= 3e+175)
		tmp = x;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.75e+71], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+175], x, N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75e71

   1. Initial program 81.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 50.6%

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

      1. associate-*r/ 61.7%

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

   7. Simplified 61.7%

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

   if -1.75e71 < y < 3.0000000000000002e175

   1. Initial program 95.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 56.6%

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

   if 3.0000000000000002e175 < y

   1. Initial program 81.8%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-/l* 93.9%

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

   7. Simplified 93.9%

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

   8. Taylor expanded in t around inf 46.7%

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

      1. associate-*l/ 46.5%

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

      2. *-commutative 46.5%

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

   10. Simplified 46.5%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+71}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.08e+71) (/ t (/ a y)) (if (<= y 1.06e+182) x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.08e+71) {
		tmp = t / (a / y);
	} else if (y <= 1.06e+182) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-1.08d+71)) then
        tmp = t / (a / y)
    else if (y <= 1.06d+182) then
        tmp = x
    else
        tmp = 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 (y <= -1.08e+71) {
		tmp = t / (a / y);
	} else if (y <= 1.06e+182) {
		tmp = x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.08e+71:
		tmp = t / (a / y)
	elif y <= 1.06e+182:
		tmp = x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.08e+71)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 1.06e+182)
		tmp = x;
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.08e+71)
		tmp = t / (a / y);
	elseif (y <= 1.06e+182)
		tmp = x;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.08e+71], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+182], x, N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08e71

   1. Initial program 81.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 50.6%

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

      1. associate-*r/ 61.7%

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

   7. Simplified 61.7%

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

      1. clear-num 61.8%

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

      2. div-inv 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -1.08e71 < y < 1.0599999999999999e182

   1. Initial program 95.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 56.6%

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

   if 1.0599999999999999e182 < y

   1. Initial program 81.8%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-/l* 93.9%

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

   7. Simplified 93.9%

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

   8. Taylor expanded in t around inf 46.7%

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

      1. associate-*l/ 46.5%

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

      2. *-commutative 46.5%

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

   10. Simplified 46.5%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+71}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+67}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.45e+67) (/ t (/ a y)) (if (<= y 2.25e+175) x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.45e+67) {
		tmp = t / (a / y);
	} else if (y <= 2.25e+175) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-2.45d+67)) then
        tmp = t / (a / y)
    else if (y <= 2.25d+175) then
        tmp = x
    else
        tmp = 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 (y <= -2.45e+67) {
		tmp = t / (a / y);
	} else if (y <= 2.25e+175) {
		tmp = x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.45e+67:
		tmp = t / (a / y)
	elif y <= 2.25e+175:
		tmp = x
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.45e+67)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 2.25e+175)
		tmp = x;
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.45e+67)
		tmp = t / (a / y);
	elseif (y <= 2.25e+175)
		tmp = x;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.45e+67], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+175], x, N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.44999999999999995e67

   1. Initial program 81.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 50.6%

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

      1. associate-*r/ 61.7%

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

   7. Simplified 61.7%

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

      1. clear-num 61.8%

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

      2. div-inv 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -2.44999999999999995e67 < y < 2.24999999999999995e175

   1. Initial program 95.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 56.6%

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

   if 2.24999999999999995e175 < y

   1. Initial program 81.8%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-/l* 93.9%

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

   7. Simplified 93.9%

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

   8. Taylor expanded in t around inf 46.7%

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

      1. associate-*l/ 46.5%

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

      2. *-commutative 46.5%

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

   10. Simplified 46.5%

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

       1. associate-*r/ 46.7%

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

       2. associate-/l* 46.5%

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

   12. Applied egg-rr 46.5%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+67}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+69}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7e+69) (/ t (/ a y)) (if (<= y 2.2e+175) x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7e+69) {
		tmp = t / (a / y);
	} else if (y <= 2.2e+175) {
		tmp = x;
	} else {
		tmp = (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 (y <= (-7d+69)) then
        tmp = t / (a / y)
    else if (y <= 2.2d+175) then
        tmp = x
    else
        tmp = (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 (y <= -7e+69) {
		tmp = t / (a / y);
	} else if (y <= 2.2e+175) {
		tmp = x;
	} else {
		tmp = (t * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7e+69:
		tmp = t / (a / y)
	elif y <= 2.2e+175:
		tmp = x
	else:
		tmp = (t * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7e+69)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 2.2e+175)
		tmp = x;
	else
		tmp = Float64(Float64(t * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7e+69)
		tmp = t / (a / y);
	elseif (y <= 2.2e+175)
		tmp = x;
	else
		tmp = (t * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7e+69], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+175], x, N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.99999999999999974e69

   1. Initial program 81.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 50.6%

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

      1. associate-*r/ 61.7%

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

   7. Simplified 61.7%

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

      1. clear-num 61.8%

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

      2. div-inv 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -6.99999999999999974e69 < y < 2.1999999999999999e175

   1. Initial program 95.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 56.6%

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

   if 2.1999999999999999e175 < y

   1. Initial program 81.8%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 46.7%

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

      1. *-commutative 46.7%

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

   7. Simplified 46.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+69}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

5. Final simplification 96.6%

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

Alternative 15: 39.6% accurate, 9.0× 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 91.2%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

5. Taylor expanded in x around inf 44.2%

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

6. Final simplification 44.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (- x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (- x (/ (* y (- z t)) a))
       (- x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / 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 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x - (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x - (y / 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 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x - (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x - (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x - Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x - Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x - (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x - (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x - N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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