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

Percentage Accurate: 92.9% → 97.9%

Time: 7.6s

Alternatives: 9

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 96.8%

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

3. Simplified 96.8%

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

   1. *-commutative 96.8%

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

   2. clear-num 96.7%

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

   3. un-div-inv 96.9%

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

5. Applied egg-rr 96.9%

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

6. Final simplification 96.9%

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

Alternative 2: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-215} \lor \neg \left(t \leq -6.8 \cdot 10^{-242}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.1e-215) (not (<= t -6.8e-242)))
   (+ x (* z (/ y t)))
   (/ (* x y) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e-215) || !(t <= -6.8e-242)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = (x * y) / -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.1d-215)) .or. (.not. (t <= (-6.8d-242)))) then
        tmp = x + (z * (y / t))
    else
        tmp = (x * y) / -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e-215) || !(t <= -6.8e-242)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = (x * y) / -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.1e-215) or not (t <= -6.8e-242):
		tmp = x + (z * (y / t))
	else:
		tmp = (x * y) / -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.1e-215) || !(t <= -6.8e-242))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(Float64(x * y) / Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.1e-215) || ~((t <= -6.8e-242)))
		tmp = x + (z * (y / t));
	else
		tmp = (x * y) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.1e-215], N[Not[LessEqual[t, -6.8e-242]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.09999999999999985e-215 or -6.8000000000000001e-242 < t

   1. Initial program 92.0%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around inf 76.9%

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

      1. associate-*l/ 79.0%

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

      2. *-commutative 79.0%

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

   6. Simplified 79.0%

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

   if -4.09999999999999985e-215 < t < -6.8000000000000001e-242

   1. Initial program 99.8%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around inf 88.4%

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

      1. distribute-lft-in 88.4%

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

      2. *-rgt-identity 88.4%

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

      3. mul-1-neg 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. unsub-neg 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in y around inf 99.8%

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

      1. associate-*r/ 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r* 88.4%

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

      4. neg-mul-1 88.4%

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

      5. distribute-neg-frac 88.4%

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

   9. Simplified 88.4%

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

       1. associate-*l/ 99.8%

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

       2. frac-2neg 99.8%

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

       3. add-sqr-sqrt 62.3%

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

       4. sqrt-unprod 50.7%

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

       5. sqr-neg 50.7%

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

       6. sqrt-unprod 0.3%

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

       7. add-sqr-sqrt 0.3%

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

       8. distribute-lft-neg-in 0.3%

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

       9. add-sqr-sqrt 0.0%

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

       10. sqrt-unprod 25.5%

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

       11. sqr-neg 25.5%

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

       12. sqrt-unprod 37.1%

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

       13. add-sqr-sqrt 99.8%

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

   11. Applied egg-rr 99.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-215} \lor \neg \left(t \leq -6.8 \cdot 10^{-242}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{-t}\\ \end{array} \]

Alternative 3: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-70} \lor \neg \left(z \leq 1.25 \cdot 10^{-61}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e-70) (not (<= z 1.25e-61)))
   (+ x (* z (/ y t)))
   (- x (* x (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-70) || !(z <= 1.25e-61)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x - (x * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.8d-70)) .or. (.not. (z <= 1.25d-61))) then
        tmp = x + (z * (y / t))
    else
        tmp = x - (x * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-70) || !(z <= 1.25e-61)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x - (x * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e-70) or not (z <= 1.25e-61):
		tmp = x + (z * (y / t))
	else:
		tmp = x - (x * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e-70) || !(z <= 1.25e-61))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x - Float64(x * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e-70) || ~((z <= 1.25e-61)))
		tmp = x + (z * (y / t));
	else
		tmp = x - (x * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e-70], N[Not[LessEqual[z, 1.25e-61]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999998e-70 or 1.25e-61 < z

   1. Initial program 89.8%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 83.8%

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

      1. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

   6. Simplified 86.2%

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

   if -3.7999999999999998e-70 < z < 1.25e-61

   1. Initial program 95.5%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 92.5%

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

      1. distribute-lft-in 92.5%

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

      2. *-rgt-identity 92.5%

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

      3. mul-1-neg 92.5%

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

      4. distribute-rgt-neg-in 92.5%

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

      5. unsub-neg 92.5%

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

   6. Simplified 92.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-70} \lor \neg \left(z \leq 1.25 \cdot 10^{-61}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.75 \cdot 10^{-215}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.75e-215)
   (+ x (/ y (/ t z)))
   (if (<= t -2.9e-243) (/ (* x y) (- t)) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.75e-215) {
		tmp = x + (y / (t / z));
	} else if (t <= -2.9e-243) {
		tmp = (x * y) / -t;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.75d-215)) then
        tmp = x + (y / (t / z))
    else if (t <= (-2.9d-243)) then
        tmp = (x * y) / -t
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.75e-215) {
		tmp = x + (y / (t / z));
	} else if (t <= -2.9e-243) {
		tmp = (x * y) / -t;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.75e-215:
		tmp = x + (y / (t / z))
	elif t <= -2.9e-243:
		tmp = (x * y) / -t
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.75e-215)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (t <= -2.9e-243)
		tmp = Float64(Float64(x * y) / Float64(-t));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.75e-215)
		tmp = x + (y / (t / z));
	elseif (t <= -2.9e-243)
		tmp = (x * y) / -t;
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.75e-215], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-243], N[(N[(x * y), $MachinePrecision] / (-t)), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.74999999999999993e-215

   1. Initial program 92.1%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 80.4%

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

   if -3.74999999999999993e-215 < t < -2.89999999999999977e-243

   1. Initial program 99.8%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around inf 88.4%

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

      1. distribute-lft-in 88.4%

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

      2. *-rgt-identity 88.4%

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

      3. mul-1-neg 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. unsub-neg 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in y around inf 99.8%

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

      1. associate-*r/ 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r* 88.4%

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

      4. neg-mul-1 88.4%

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

      5. distribute-neg-frac 88.4%

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

   9. Simplified 88.4%

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

       1. associate-*l/ 99.8%

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

       2. frac-2neg 99.8%

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

       3. add-sqr-sqrt 62.3%

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

       4. sqrt-unprod 50.7%

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

       5. sqr-neg 50.7%

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

       6. sqrt-unprod 0.3%

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

       7. add-sqr-sqrt 0.3%

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

       8. distribute-lft-neg-in 0.3%

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

       9. add-sqr-sqrt 0.0%

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

       10. sqrt-unprod 25.5%

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

       11. sqr-neg 25.5%

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

       12. sqrt-unprod 37.1%

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

       13. add-sqr-sqrt 99.8%

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

   11. Applied egg-rr 99.8%

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

   if -2.89999999999999977e-243 < t

   1. Initial program 91.9%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around inf 74.5%

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

      1. associate-*l/ 77.8%

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

      2. *-commutative 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.75 \cdot 10^{-215}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5: 50.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+54} \lor \neg \left(y \leq 1.75 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.55e+54) (not (<= y 1.75e+19))) (* y (/ (- x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e+54) || !(y <= 1.75e+19)) {
		tmp = y * (-x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.55d+54)) .or. (.not. (y <= 1.75d+19))) then
        tmp = y * (-x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e+54) || !(y <= 1.75e+19)) {
		tmp = y * (-x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.55e+54) or not (y <= 1.75e+19):
		tmp = y * (-x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.55e+54) || !(y <= 1.75e+19))
		tmp = Float64(y * Float64(Float64(-x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.55e+54) || ~((y <= 1.75e+19)))
		tmp = y * (-x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.55e+54], N[Not[LessEqual[y, 1.75e+19]], $MachinePrecision]], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e54 or 1.75e19 < y

   1. Initial program 85.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 58.5%

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

      1. distribute-lft-in 58.5%

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

      2. *-rgt-identity 58.5%

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

      3. mul-1-neg 58.5%

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

      4. distribute-rgt-neg-in 58.5%

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

      5. unsub-neg 58.5%

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

   6. Simplified 58.5%

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

      1. *-commutative 58.5%

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

      2. add-sqr-sqrt 29.2%

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

      3. sqrt-unprod 38.4%

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

      4. sqr-neg 38.4%

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

      5. sqrt-unprod 12.1%

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

      6. add-sqr-sqrt 23.2%

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

      7. associate-/r/ 20.1%

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

      8. add-sqr-sqrt 9.7%

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

      9. sqrt-unprod 39.2%

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

      10. sqr-neg 39.2%

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

      11. sqrt-unprod 28.4%

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

      12. add-sqr-sqrt 57.7%

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

   8. Applied egg-rr 57.7%

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

   9. Taylor expanded in y around inf 45.3%

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

       1. mul-1-neg 45.3%

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

       2. associate-*l/ 45.1%

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

       3. distribute-lft-neg-out 45.1%

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

       4. *-commutative 45.1%

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

       5. distribute-neg-frac 45.1%

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

   11. Simplified 45.1%

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

   if -1.55e54 < y < 1.75e19

   1. Initial program 97.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 61.6%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+54} \lor \neg \left(y \leq 1.75 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+55} \lor \neg \left(y \leq 1.6 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.8e+55) (not (<= y 1.6e+20))) (* x (/ (- y) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.8e+55) || !(y <= 1.6e+20)) {
		tmp = x * (-y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.8d+55)) .or. (.not. (y <= 1.6d+20))) then
        tmp = x * (-y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.8e+55) || !(y <= 1.6e+20)) {
		tmp = x * (-y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.8e+55) or not (y <= 1.6e+20):
		tmp = x * (-y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.8e+55) || !(y <= 1.6e+20))
		tmp = Float64(x * Float64(Float64(-y) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.8e+55) || ~((y <= 1.6e+20)))
		tmp = x * (-y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.8e+55], N[Not[LessEqual[y, 1.6e+20]], $MachinePrecision]], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.8000000000000001e55 or 1.6e20 < y

   1. Initial program 85.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 58.5%

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

      1. distribute-lft-in 58.5%

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

      2. *-rgt-identity 58.5%

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

      3. mul-1-neg 58.5%

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

      4. distribute-rgt-neg-in 58.5%

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

      5. unsub-neg 58.5%

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

   6. Simplified 58.5%

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

   7. Taylor expanded in y around inf 45.3%

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

      1. associate-*r/ 46.0%

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

      2. *-commutative 46.0%

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

      3. associate-*r* 46.0%

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

      4. neg-mul-1 46.0%

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

      5. distribute-neg-frac 46.0%

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

   9. Simplified 46.0%

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

   if -2.8000000000000001e55 < y < 1.6e20

   1. Initial program 97.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 61.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+55} \lor \neg \left(y \leq 1.6 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+52} \lor \neg \left(y \leq 2.3 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{-x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e+52) (not (<= y 2.3e+22))) (/ (- x) (/ t y)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e+52) || !(y <= 2.3e+22)) {
		tmp = -x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.4d+52)) .or. (.not. (y <= 2.3d+22))) then
        tmp = -x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e+52) || !(y <= 2.3e+22)) {
		tmp = -x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e+52) or not (y <= 2.3e+22):
		tmp = -x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e+52) || !(y <= 2.3e+22))
		tmp = Float64(Float64(-x) / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.4e+52) || ~((y <= 2.3e+22)))
		tmp = -x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.4e+52], N[Not[LessEqual[y, 2.3e+22]], $MachinePrecision]], N[((-x) / N[(t / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e52 or 2.3000000000000002e22 < y

   1. Initial program 85.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 58.5%

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

      1. distribute-lft-in 58.5%

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

      2. *-rgt-identity 58.5%

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

      3. mul-1-neg 58.5%

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

      4. distribute-rgt-neg-in 58.5%

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

      5. unsub-neg 58.5%

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

   6. Simplified 58.5%

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

   7. Taylor expanded in y around inf 45.3%

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

      1. associate-*r/ 46.0%

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

      2. *-commutative 46.0%

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

      3. associate-*r* 46.0%

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

      4. neg-mul-1 46.0%

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

      5. distribute-neg-frac 46.0%

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

   9. Simplified 46.0%

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

       1. associate-*l/ 45.3%

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

       2. distribute-lft-neg-in 45.3%

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

       3. *-commutative 45.3%

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

       4. distribute-neg-frac 45.3%

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

       5. associate-/l* 46.2%

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

       6. distribute-neg-frac 46.2%

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

   11. Applied egg-rr 46.2%

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

   if -2.4e52 < y < 2.3000000000000002e22

   1. Initial program 97.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 61.6%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+52} \lor \neg \left(y \leq 2.3 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{-x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 96.8%

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

3. Simplified 96.8%

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

4. Final simplification 96.8%

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

Alternative 9: 38.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 96.8%

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

3. Simplified 96.8%

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

4. Taylor expanded in y around 0 41.0%

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

5. Final simplification 41.0%

   \[\leadsto x \]

Developer target: 91.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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