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

Percentage Accurate: 93.5% → 97.4%

Time: 11.8s

Alternatives: 11

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: 93.5% 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 92.1%

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

   1. associate-/l* 94.0%

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

   2. cancel-sign-sub-inv 94.0%

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

   3. associate-/l* 92.1%

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

   4. distribute-lft-neg-out 92.1%

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

   5. distribute-rgt-neg-in 92.1%

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

   6. associate-*l/ 98.1%

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

   7. sub-neg 98.1%

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

   8. distribute-neg-in 98.1%

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

   9. remove-double-neg 98.1%

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

   10. +-commutative 98.1%

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

   11. sub-neg 98.1%

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

3. Simplified 98.1%

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

   1. *-commutative 98.1%

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

   2. clear-num 98.1%

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

   3. un-div-inv 98.2%

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

6. Applied egg-rr 98.2%

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

7. Final simplification 98.2%

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

Alternative 2: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-8} \lor \neg \left(t \leq 3.3 \cdot 10^{+36}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e-8) (not (<= t 3.3e+36)))
   (+ x (/ t (/ a y)))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e-8) || !(t <= 3.3e+36)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.2d-8)) .or. (.not. (t <= 3.3d+36))) then
        tmp = x + (t / (a / y))
    else
        tmp = x - (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e-8) || !(t <= 3.3e+36)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e-8) or not (t <= 3.3e+36):
		tmp = x + (t / (a / y))
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e-8) || !(t <= 3.3e+36))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e-8) || ~((t <= 3.3e+36)))
		tmp = x + (t / (a / y));
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e-8], N[Not[LessEqual[t, 3.3e+36]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.19999999999999999e-8 or 3.2999999999999999e36 < t

   1. Initial program 87.9%

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

      1. associate-/l* 93.4%

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

      2. cancel-sign-sub-inv 93.4%

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

      3. associate-/l* 87.9%

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

      4. distribute-lft-neg-out 87.9%

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

      5. distribute-rgt-neg-in 87.9%

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

      6. associate-*l/ 99.1%

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

      7. sub-neg 99.1%

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

      8. distribute-neg-in 99.1%

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

      9. remove-double-neg 99.1%

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

      10. +-commutative 99.1%

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

      11. sub-neg 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. *-commutative 79.6%

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

   7. Simplified 79.6%

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

      1. div-inv 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*l* 86.9%

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

      4. div-inv 86.9%

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

   9. Applied egg-rr 86.9%

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

       1. clear-num 54.9%

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

       2. un-div-inv 55.0%

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

   11. Applied egg-rr 87.0%

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

   if -1.19999999999999999e-8 < t < 3.2999999999999999e36

   1. Initial program 95.6%

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

      1. associate-/l* 94.5%

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

      2. cancel-sign-sub-inv 94.5%

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

      3. associate-/l* 95.6%

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

      4. distribute-lft-neg-out 95.6%

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

      5. distribute-rgt-neg-in 95.6%

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

      6. associate-*l/ 97.3%

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

      7. sub-neg 97.3%

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

      8. distribute-neg-in 97.3%

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

      9. remove-double-neg 97.3%

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

      10. +-commutative 97.3%

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

      11. sub-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. sub-neg 87.7%

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

      3. associate-/l* 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-8} \lor \neg \left(t \leq 3.3 \cdot 10^{+36}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.00039 \lor \neg \left(t \leq 4.5 \cdot 10^{+39}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.00039) (not (<= t 4.5e+39)))
   (+ x (/ t (/ a y)))
   (- x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.00039) || !(t <= 4.5e+39)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x - (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 ((t <= (-0.00039d0)) .or. (.not. (t <= 4.5d+39))) then
        tmp = x + (t / (a / y))
    else
        tmp = x - (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 ((t <= -0.00039) || !(t <= 4.5e+39)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x - (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.00039) or not (t <= 4.5e+39):
		tmp = x + (t / (a / y))
	else:
		tmp = x - (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.00039) || !(t <= 4.5e+39))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x - Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.00039) || ~((t <= 4.5e+39)))
		tmp = x + (t / (a / y));
	else
		tmp = x - (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.00039], N[Not[LessEqual[t, 4.5e+39]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.89999999999999993e-4 or 4.49999999999999996e39 < t

   1. Initial program 87.9%

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

      1. associate-/l* 93.4%

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

      2. cancel-sign-sub-inv 93.4%

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

      3. associate-/l* 87.9%

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

      4. distribute-lft-neg-out 87.9%

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

      5. distribute-rgt-neg-in 87.9%

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

      6. associate-*l/ 99.1%

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

      7. sub-neg 99.1%

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

      8. distribute-neg-in 99.1%

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

      9. remove-double-neg 99.1%

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

      10. +-commutative 99.1%

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

      11. sub-neg 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. *-commutative 79.6%

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

   7. Simplified 79.6%

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

      1. div-inv 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*l* 86.9%

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

      4. div-inv 86.9%

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

   9. Applied egg-rr 86.9%

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

       1. clear-num 54.9%

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

       2. un-div-inv 55.0%

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

   11. Applied egg-rr 87.0%

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

   if -3.89999999999999993e-4 < t < 4.49999999999999996e39

   1. Initial program 95.6%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. div-inv 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*l* 90.7%

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

      4. div-inv 90.8%

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

   7. Applied egg-rr 90.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00039 \lor \neg \left(t \leq 4.5 \cdot 10^{+39}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+110}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+202}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+110)
   (/ (- z) (/ a y))
   (if (<= z 2.45e+202) (+ x (* t (/ y a))) (* z (/ y (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+110) {
		tmp = -z / (a / y);
	} else if (z <= 2.45e+202) {
		tmp = x + (t * (y / 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) :: tmp
    if (z <= (-4.3d+110)) then
        tmp = -z / (a / y)
    else if (z <= 2.45d+202) then
        tmp = x + (t * (y / 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 tmp;
	if (z <= -4.3e+110) {
		tmp = -z / (a / y);
	} else if (z <= 2.45e+202) {
		tmp = x + (t * (y / a));
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+110:
		tmp = -z / (a / y)
	elif z <= 2.45e+202:
		tmp = x + (t * (y / a))
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+110)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= 2.45e+202)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 <= -4.3e+110)
		tmp = -z / (a / y);
	elseif (z <= 2.45e+202)
		tmp = x + (t * (y / a));
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+110], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+202], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.30000000000000007e110

   1. Initial program 83.1%

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

      1. associate-/l* 90.2%

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

      2. cancel-sign-sub-inv 90.2%

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

      3. associate-/l* 83.1%

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

      4. distribute-lft-neg-out 83.1%

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

      5. distribute-rgt-neg-in 83.1%

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

      6. associate-*l/ 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

   3. Simplified 99.7%

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

      1. *-un-lft-identity 99.7%

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

      2. *-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. *-rgt-identity 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in z around inf 68.1%

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

       1. mul-1-neg 68.1%

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

       2. distribute-frac-neg2 68.1%

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

       3. associate-*r/ 73.0%

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

   11. Simplified 73.0%

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

       1. associate-*r/ 68.1%

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

       2. *-commutative 68.1%

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

       3. distribute-frac-neg2 68.1%

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

       4. associate-*r/ 80.1%

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

       5. distribute-lft-neg-in 80.1%

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

       6. clear-num 80.0%

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

       7. un-div-inv 80.1%

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

   13. Applied egg-rr 80.1%

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

   if -4.30000000000000007e110 < z < 2.45e202

   1. Initial program 94.3%

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

      1. associate-/l* 96.9%

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

      2. cancel-sign-sub-inv 96.9%

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

      3. associate-/l* 94.3%

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

      4. distribute-lft-neg-out 94.3%

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

      5. distribute-rgt-neg-in 94.3%

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

      6. associate-*l/ 98.1%

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

      7. sub-neg 98.1%

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

      8. distribute-neg-in 98.1%

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

      9. remove-double-neg 98.1%

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

      10. +-commutative 98.1%

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

      11. sub-neg 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. *-commutative 79.7%

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

   7. Simplified 79.7%

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

      1. div-inv 79.7%

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

      2. *-commutative 79.7%

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

      3. associate-*l* 84.1%

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

      4. div-inv 84.1%

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

   9. Applied egg-rr 84.1%

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

   if 2.45e202 < z

   1. Initial program 88.4%

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

      1. associate-/l* 76.6%

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

      2. cancel-sign-sub-inv 76.6%

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

      3. associate-/l* 88.4%

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

      4. distribute-lft-neg-out 88.4%

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

      5. distribute-rgt-neg-in 88.4%

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

      6. associate-*l/ 95.9%

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

      7. sub-neg 95.9%

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

      8. distribute-neg-in 95.9%

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

      9. remove-double-neg 95.9%

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

      10. +-commutative 95.9%

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

      11. sub-neg 95.9%

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

   3. Simplified 95.9%

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

      1. *-un-lft-identity 95.9%

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

      2. *-commutative 95.9%

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

      3. +-commutative 95.9%

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

      4. fma-define 95.9%

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

   6. Applied egg-rr 95.9%

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

      1. *-rgt-identity 95.9%

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

   8. Simplified 95.9%

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

   9. Taylor expanded in z around inf 76.5%

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

       1. mul-1-neg 76.5%

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

       2. distribute-frac-neg2 76.5%

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

       3. associate-*r/ 72.2%

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

   11. Simplified 72.2%

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

       1. associate-*r/ 76.5%

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

       2. *-commutative 76.5%

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

       3. distribute-frac-neg2 76.5%

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

       4. associate-*r/ 83.8%

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

   13. Applied egg-rr 83.8%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+110}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+202}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+202}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.3e+106)
   (/ (- z) (/ a y))
   (if (<= z 2.1e+202) (+ x (/ t (/ a y))) (* z (/ y (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.3e+106) {
		tmp = -z / (a / y);
	} else if (z <= 2.1e+202) {
		tmp = x + (t / (a / y));
	} 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 <= (-6.3d+106)) then
        tmp = -z / (a / y)
    else if (z <= 2.1d+202) then
        tmp = x + (t / (a / y))
    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 <= -6.3e+106) {
		tmp = -z / (a / y);
	} else if (z <= 2.1e+202) {
		tmp = x + (t / (a / y));
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.3e+106:
		tmp = -z / (a / y)
	elif z <= 2.1e+202:
		tmp = x + (t / (a / y))
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.3e+106)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= 2.1e+202)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	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 <= -6.3e+106)
		tmp = -z / (a / y);
	elseif (z <= 2.1e+202)
		tmp = x + (t / (a / y));
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.3e+106], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+202], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.29999999999999974e106

   1. Initial program 83.1%

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

      1. associate-/l* 90.2%

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

      2. cancel-sign-sub-inv 90.2%

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

      3. associate-/l* 83.1%

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

      4. distribute-lft-neg-out 83.1%

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

      5. distribute-rgt-neg-in 83.1%

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

      6. associate-*l/ 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

   3. Simplified 99.7%

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

      1. *-un-lft-identity 99.7%

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

      2. *-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. *-rgt-identity 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in z around inf 68.1%

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

       1. mul-1-neg 68.1%

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

       2. distribute-frac-neg2 68.1%

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

       3. associate-*r/ 73.0%

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

   11. Simplified 73.0%

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

       1. associate-*r/ 68.1%

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

       2. *-commutative 68.1%

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

       3. distribute-frac-neg2 68.1%

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

       4. associate-*r/ 80.1%

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

       5. distribute-lft-neg-in 80.1%

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

       6. clear-num 80.0%

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

       7. un-div-inv 80.1%

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

   13. Applied egg-rr 80.1%

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

   if -6.29999999999999974e106 < z < 2.1e202

   1. Initial program 94.3%

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

      1. associate-/l* 96.9%

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

      2. cancel-sign-sub-inv 96.9%

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

      3. associate-/l* 94.3%

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

      4. distribute-lft-neg-out 94.3%

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

      5. distribute-rgt-neg-in 94.3%

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

      6. associate-*l/ 98.1%

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

      7. sub-neg 98.1%

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

      8. distribute-neg-in 98.1%

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

      9. remove-double-neg 98.1%

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

      10. +-commutative 98.1%

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

      11. sub-neg 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. *-commutative 79.7%

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

   7. Simplified 79.7%

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

      1. div-inv 79.7%

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

      2. *-commutative 79.7%

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

      3. associate-*l* 84.1%

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

      4. div-inv 84.1%

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

   9. Applied egg-rr 84.1%

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

       1. clear-num 37.9%

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

       2. un-div-inv 38.0%

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

   11. Applied egg-rr 84.2%

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

   if 2.1e202 < z

   1. Initial program 88.4%

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

      1. associate-/l* 76.6%

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

      2. cancel-sign-sub-inv 76.6%

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

      3. associate-/l* 88.4%

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

      4. distribute-lft-neg-out 88.4%

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

      5. distribute-rgt-neg-in 88.4%

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

      6. associate-*l/ 95.9%

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

      7. sub-neg 95.9%

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

      8. distribute-neg-in 95.9%

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

      9. remove-double-neg 95.9%

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

      10. +-commutative 95.9%

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

      11. sub-neg 95.9%

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

   3. Simplified 95.9%

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

      1. *-un-lft-identity 95.9%

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

      2. *-commutative 95.9%

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

      3. +-commutative 95.9%

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

      4. fma-define 95.9%

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

   6. Applied egg-rr 95.9%

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

      1. *-rgt-identity 95.9%

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

   8. Simplified 95.9%

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

   9. Taylor expanded in z around inf 76.5%

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

       1. mul-1-neg 76.5%

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

       2. distribute-frac-neg2 76.5%

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

       3. associate-*r/ 72.2%

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

   11. Simplified 72.2%

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

       1. associate-*r/ 76.5%

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

       2. *-commutative 76.5%

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

       3. distribute-frac-neg2 76.5%

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

       4. associate-*r/ 83.8%

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

   13. Applied egg-rr 83.8%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+202}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 470000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.8e-58)
   (* t (/ y a))
   (if (<= y 470000000000.0) x (* z (/ y (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.8e-58) {
		tmp = t * (y / a);
	} else if (y <= 470000000000.0) {
		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 (y <= (-2.8d-58)) then
        tmp = t * (y / a)
    else if (y <= 470000000000.0d0) 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 (y <= -2.8e-58) {
		tmp = t * (y / a);
	} else if (y <= 470000000000.0) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.8e-58:
		tmp = t * (y / a)
	elif y <= 470000000000.0:
		tmp = x
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.8e-58)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 470000000000.0)
		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 (y <= -2.8e-58)
		tmp = t * (y / a);
	elseif (y <= 470000000000.0)
		tmp = x;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.8e-58], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 470000000000.0], x, N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000001e-58

   1. Initial program 89.3%

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

      1. associate-/l* 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. associate-/l* 89.3%

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

      4. distribute-lft-neg-out 89.3%

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

      5. distribute-rgt-neg-in 89.3%

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

      6. associate-*l/ 98.5%

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

      7. sub-neg 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. remove-double-neg 98.5%

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

      10. +-commutative 98.5%

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

      11. sub-neg 98.5%

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

   3. Simplified 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. fma-define 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. *-rgt-identity 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in t around inf 41.3%

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

       1. associate-/l* 48.9%

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

   11. Simplified 48.9%

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

   if -2.8000000000000001e-58 < y < 4.7e11

   1. Initial program 99.5%

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

      1. associate-/l* 86.6%

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

      2. cancel-sign-sub-inv 86.6%

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

      3. associate-/l* 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. associate-*l/ 97.6%

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

      7. sub-neg 97.6%

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

      8. distribute-neg-in 97.6%

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

      9. remove-double-neg 97.6%

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

      10. +-commutative 97.6%

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

      11. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf 62.8%

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

   if 4.7e11 < y

   1. Initial program 83.7%

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

      1. associate-/l* 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. associate-/l* 83.7%

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

      4. distribute-lft-neg-out 83.7%

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

      5. distribute-rgt-neg-in 83.7%

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

      6. associate-*l/ 98.5%

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

      7. sub-neg 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. remove-double-neg 98.5%

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

      10. +-commutative 98.5%

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

      11. sub-neg 98.5%

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

   3. Simplified 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. fma-define 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. *-rgt-identity 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in z around inf 44.1%

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

       1. mul-1-neg 44.1%

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

       2. distribute-frac-neg2 44.1%

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

       3. associate-*r/ 51.0%

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

   11. Simplified 51.0%

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

       1. associate-*r/ 44.1%

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

       2. *-commutative 44.1%

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

       3. distribute-frac-neg2 44.1%

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

       4. associate-*r/ 51.0%

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

   13. Applied egg-rr 51.0%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 470000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 23000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.3e-58)
   (* t (/ y a))
   (if (<= y 23000000000.0) x (* y (/ (- z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.3e-58) {
		tmp = t * (y / a);
	} else if (y <= 23000000000.0) {
		tmp = x;
	} else {
		tmp = y * (-z / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.3d-58)) then
        tmp = t * (y / a)
    else if (y <= 23000000000.0d0) then
        tmp = x
    else
        tmp = y * (-z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.3e-58) {
		tmp = t * (y / a);
	} else if (y <= 23000000000.0) {
		tmp = x;
	} else {
		tmp = y * (-z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.3e-58:
		tmp = t * (y / a)
	elif y <= 23000000000.0:
		tmp = x
	else:
		tmp = y * (-z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.3e-58)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 23000000000.0)
		tmp = x;
	else
		tmp = Float64(y * Float64(Float64(-z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.3e-58)
		tmp = t * (y / a);
	elseif (y <= 23000000000.0)
		tmp = x;
	else
		tmp = y * (-z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.3e-58], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 23000000000.0], x, N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2999999999999999e-58

   1. Initial program 89.3%

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

      1. associate-/l* 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. associate-/l* 89.3%

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

      4. distribute-lft-neg-out 89.3%

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

      5. distribute-rgt-neg-in 89.3%

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

      6. associate-*l/ 98.5%

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

      7. sub-neg 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. remove-double-neg 98.5%

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

      10. +-commutative 98.5%

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

      11. sub-neg 98.5%

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

   3. Simplified 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. fma-define 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. *-rgt-identity 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in t around inf 41.3%

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

       1. associate-/l* 48.9%

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

   11. Simplified 48.9%

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

   if -4.2999999999999999e-58 < y < 2.3e10

   1. Initial program 99.5%

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

      1. associate-/l* 86.6%

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

      2. cancel-sign-sub-inv 86.6%

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

      3. associate-/l* 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. associate-*l/ 97.6%

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

      7. sub-neg 97.6%

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

      8. distribute-neg-in 97.6%

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

      9. remove-double-neg 97.6%

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

      10. +-commutative 97.6%

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

      11. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf 62.8%

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

   if 2.3e10 < y

   1. Initial program 83.7%

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

      1. associate-/l* 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. associate-/l* 83.7%

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

      4. distribute-lft-neg-out 83.7%

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

      5. distribute-rgt-neg-in 83.7%

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

      6. associate-*l/ 98.5%

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

      7. sub-neg 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. remove-double-neg 98.5%

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

      10. +-commutative 98.5%

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

      11. sub-neg 98.5%

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

   3. Simplified 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. fma-define 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. *-rgt-identity 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in z around inf 44.1%

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

       1. mul-1-neg 44.1%

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

       2. distribute-frac-neg2 44.1%

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

       3. associate-*r/ 51.0%

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

   11. Simplified 51.0%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 23000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-57} \lor \neg \left(y \leq 16500000000000\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e-57) (not (<= y 16500000000000.0))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-57) || !(y <= 16500000000000.0)) {
		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 <= (-2.9d-57)) .or. (.not. (y <= 16500000000000.0d0))) 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 <= -2.9e-57) || !(y <= 16500000000000.0)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e-57) or not (y <= 16500000000000.0):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e-57) || !(y <= 16500000000000.0))
		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 <= -2.9e-57) || ~((y <= 16500000000000.0)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e-57], N[Not[LessEqual[y, 16500000000000.0]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.90000000000000025e-57 or 1.65e13 < y

   1. Initial program 86.1%

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

      1. associate-/l* 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. associate-/l* 86.1%

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

      4. distribute-lft-neg-out 86.1%

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

      5. distribute-rgt-neg-in 86.1%

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

      6. associate-*l/ 98.5%

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

      7. sub-neg 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. remove-double-neg 98.5%

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

      10. +-commutative 98.5%

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

      11. sub-neg 98.5%

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

   3. Simplified 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. fma-define 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. *-rgt-identity 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in t around inf 36.5%

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

       1. associate-/l* 43.0%

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

   11. Simplified 43.0%

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

   if -2.90000000000000025e-57 < y < 1.65e13

   1. Initial program 99.5%

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

      1. associate-/l* 86.6%

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

      2. cancel-sign-sub-inv 86.6%

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

      3. associate-/l* 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. associate-*l/ 97.6%

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

      7. sub-neg 97.6%

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

      8. distribute-neg-in 97.6%

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

      9. remove-double-neg 97.6%

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

      10. +-commutative 97.6%

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

      11. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf 62.8%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-57} \lor \neg \left(y \leq 16500000000000\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 17000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.3e-57)
   (* t (/ y a))
   (if (<= y 17000000000000.0) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.3e-57) {
		tmp = t * (y / a);
	} else if (y <= 17000000000000.0) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-3.3d-57)) then
        tmp = t * (y / a)
    else if (y <= 17000000000000.0d0) then
        tmp = x
    else
        tmp = 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 (y <= -3.3e-57) {
		tmp = t * (y / a);
	} else if (y <= 17000000000000.0) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.3e-57:
		tmp = t * (y / a)
	elif y <= 17000000000000.0:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.3e-57)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 17000000000000.0)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.3e-57)
		tmp = t * (y / a);
	elseif (y <= 17000000000000.0)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.3e-57], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 17000000000000.0], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2999999999999998e-57

   1. Initial program 89.3%

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

      1. associate-/l* 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. associate-/l* 89.3%

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

      4. distribute-lft-neg-out 89.3%

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

      5. distribute-rgt-neg-in 89.3%

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

      6. associate-*l/ 98.5%

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

      7. sub-neg 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. remove-double-neg 98.5%

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

      10. +-commutative 98.5%

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

      11. sub-neg 98.5%

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

   3. Simplified 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. fma-define 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. *-rgt-identity 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in t around inf 41.3%

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

       1. associate-/l* 48.9%

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

   11. Simplified 48.9%

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

   if -3.2999999999999998e-57 < y < 1.7e13

   1. Initial program 99.5%

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

      1. associate-/l* 86.6%

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

      2. cancel-sign-sub-inv 86.6%

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

      3. associate-/l* 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. associate-*l/ 97.6%

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

      7. sub-neg 97.6%

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

      8. distribute-neg-in 97.6%

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

      9. remove-double-neg 97.6%

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

      10. +-commutative 97.6%

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

      11. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf 62.8%

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

   if 1.7e13 < y

   1. Initial program 83.7%

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

      1. associate-/l* 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. associate-/l* 83.7%

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

      4. distribute-lft-neg-out 83.7%

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

      5. distribute-rgt-neg-in 83.7%

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

      6. associate-*l/ 98.5%

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

      7. sub-neg 98.5%

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

      8. distribute-neg-in 98.5%

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

      9. remove-double-neg 98.5%

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

      10. +-commutative 98.5%

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

      11. sub-neg 98.5%

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

   3. Simplified 98.5%

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

      1. *-un-lft-identity 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. fma-define 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. *-rgt-identity 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in t around inf 32.8%

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

       1. associate-/l* 38.5%

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

   11. Simplified 38.5%

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

       1. clear-num 38.5%

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

       2. un-div-inv 38.6%

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

   13. Applied egg-rr 38.6%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 17000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. associate-/l* 94.0%

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

   2. cancel-sign-sub-inv 94.0%

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

   3. associate-/l* 92.1%

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

   4. distribute-lft-neg-out 92.1%

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

   5. distribute-rgt-neg-in 92.1%

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

   6. associate-*l/ 98.1%

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

   7. sub-neg 98.1%

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

   8. distribute-neg-in 98.1%

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

   9. remove-double-neg 98.1%

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

   10. +-commutative 98.1%

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

   11. sub-neg 98.1%

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

3. Simplified 98.1%

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

5. Final simplification 98.1%

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

Alternative 11: 39.9% 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 92.1%

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

   1. associate-/l* 94.0%

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

   2. cancel-sign-sub-inv 94.0%

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

   3. associate-/l* 92.1%

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

   4. distribute-lft-neg-out 92.1%

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

   5. distribute-rgt-neg-in 92.1%

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

   6. associate-*l/ 98.1%

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

   7. sub-neg 98.1%

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

   8. distribute-neg-in 98.1%

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

   9. remove-double-neg 98.1%

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

   10. +-commutative 98.1%

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

   11. sub-neg 98.1%

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

3. Simplified 98.1%

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

5. Taylor expanded in x around inf 38.5%

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

6. Final simplification 38.5%

   \[\leadsto x \]
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 2024048 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (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)))