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

Percentage Accurate: 92.8% → 98.0%

Time: 8.1s

Alternatives: 10

Speedup: 1.0×

• 24.8% 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: 92.8% 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: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{t}, z - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. +-commutative 92.7%

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

   2. associate-*l/ 98.1%

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

   3. fma-def 98.1%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 2: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-47}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.2e+61)
   x
   (if (<= t -3.15e-52)
     (* y (/ (- x) t))
     (if (<= t -4e-107) x (if (<= t 1.35e-47) (* (/ y t) (- x)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e+61) {
		tmp = x;
	} else if (t <= -3.15e-52) {
		tmp = y * (-x / t);
	} else if (t <= -4e-107) {
		tmp = x;
	} else if (t <= 1.35e-47) {
		tmp = (y / t) * -x;
	} 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 (t <= (-5.2d+61)) then
        tmp = x
    else if (t <= (-3.15d-52)) then
        tmp = y * (-x / t)
    else if (t <= (-4d-107)) then
        tmp = x
    else if (t <= 1.35d-47) then
        tmp = (y / t) * -x
    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 (t <= -5.2e+61) {
		tmp = x;
	} else if (t <= -3.15e-52) {
		tmp = y * (-x / t);
	} else if (t <= -4e-107) {
		tmp = x;
	} else if (t <= 1.35e-47) {
		tmp = (y / t) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.2e+61:
		tmp = x
	elif t <= -3.15e-52:
		tmp = y * (-x / t)
	elif t <= -4e-107:
		tmp = x
	elif t <= 1.35e-47:
		tmp = (y / t) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.2e+61)
		tmp = x;
	elseif (t <= -3.15e-52)
		tmp = Float64(y * Float64(Float64(-x) / t));
	elseif (t <= -4e-107)
		tmp = x;
	elseif (t <= 1.35e-47)
		tmp = Float64(Float64(y / t) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.2e+61)
		tmp = x;
	elseif (t <= -3.15e-52)
		tmp = y * (-x / t);
	elseif (t <= -4e-107)
		tmp = x;
	elseif (t <= 1.35e-47)
		tmp = (y / t) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.2e+61], x, If[LessEqual[t, -3.15e-52], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-107], x, If[LessEqual[t, 1.35e-47], N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.19999999999999945e61 or -3.1500000000000002e-52 < t < -4e-107 or 1.3499999999999999e-47 < t

   1. Initial program 87.4%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around 0 66.0%

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

   if -5.19999999999999945e61 < t < -3.1500000000000002e-52

   1. Initial program 99.9%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. unsub-neg 40.5%

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

   6. Simplified 40.5%

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

   7. Taylor expanded in y around inf 28.7%

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

      1. mul-1-neg 28.7%

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

      2. distribute-frac-neg 28.7%

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

   9. Simplified 28.7%

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

   10. Taylor expanded in x around 0 32.4%

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

       1. associate-*r/ 32.4%

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

       2. *-commutative 32.4%

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

       3. neg-mul-1 32.4%

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

       4. distribute-rgt-neg-out 32.4%

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

       5. associate-*r/ 32.4%

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

   12. Simplified 32.4%

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

   if -4e-107 < t < 1.3499999999999999e-47

   1. Initial program 98.7%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in y around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. distribute-frac-neg 48.7%

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

   9. Simplified 48.7%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-47}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.5e+62)
   x
   (if (<= t -2.85e-52)
     (* y (/ (- x) t))
     (if (<= t -3.5e-107) x (if (<= t 2.4e-48) (/ x (/ (- t) y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.5e+62) {
		tmp = x;
	} else if (t <= -2.85e-52) {
		tmp = y * (-x / t);
	} else if (t <= -3.5e-107) {
		tmp = x;
	} else if (t <= 2.4e-48) {
		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 (t <= (-7.5d+62)) then
        tmp = x
    else if (t <= (-2.85d-52)) then
        tmp = y * (-x / t)
    else if (t <= (-3.5d-107)) then
        tmp = x
    else if (t <= 2.4d-48) 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 (t <= -7.5e+62) {
		tmp = x;
	} else if (t <= -2.85e-52) {
		tmp = y * (-x / t);
	} else if (t <= -3.5e-107) {
		tmp = x;
	} else if (t <= 2.4e-48) {
		tmp = x / (-t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.5e+62:
		tmp = x
	elif t <= -2.85e-52:
		tmp = y * (-x / t)
	elif t <= -3.5e-107:
		tmp = x
	elif t <= 2.4e-48:
		tmp = x / (-t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.5e+62)
		tmp = x;
	elseif (t <= -2.85e-52)
		tmp = Float64(y * Float64(Float64(-x) / t));
	elseif (t <= -3.5e-107)
		tmp = x;
	elseif (t <= 2.4e-48)
		tmp = Float64(x / Float64(Float64(-t) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7.5e+62)
		tmp = x;
	elseif (t <= -2.85e-52)
		tmp = y * (-x / t);
	elseif (t <= -3.5e-107)
		tmp = x;
	elseif (t <= 2.4e-48)
		tmp = x / (-t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.5e+62], x, If[LessEqual[t, -2.85e-52], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-107], x, If[LessEqual[t, 2.4e-48], N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999998e62 or -2.8499999999999999e-52 < t < -3.49999999999999985e-107 or 2.4e-48 < t

   1. Initial program 87.4%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around 0 66.0%

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

   if -7.49999999999999998e62 < t < -2.8499999999999999e-52

   1. Initial program 99.9%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. unsub-neg 40.5%

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

   6. Simplified 40.5%

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

   7. Taylor expanded in y around inf 28.7%

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

      1. mul-1-neg 28.7%

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

      2. distribute-frac-neg 28.7%

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

   9. Simplified 28.7%

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

   10. Taylor expanded in x around 0 32.4%

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

       1. associate-*r/ 32.4%

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

       2. *-commutative 32.4%

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

       3. neg-mul-1 32.4%

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

       4. distribute-rgt-neg-out 32.4%

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

       5. associate-*r/ 32.4%

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

   12. Simplified 32.4%

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

   if -3.49999999999999985e-107 < t < 2.4e-48

   1. Initial program 98.7%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in y around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. distribute-frac-neg 48.7%

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

   9. Simplified 48.7%

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

   10. Taylor expanded in x around 0 42.7%

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

       1. associate-*r/ 42.7%

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

       2. *-commutative 42.7%

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

       3. neg-mul-1 42.7%

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

       4. distribute-rgt-neg-out 42.7%

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

       5. associate-*r/ 38.3%

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

   12. Simplified 38.3%

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

       1. *-commutative 38.3%

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

       2. distribute-frac-neg 38.3%

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

       3. distribute-lft-neg-in 38.3%

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

       4. associate-/r/ 48.8%

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

       5. frac-2neg 48.8%

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

       6. distribute-neg-frac 48.8%

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

       7. remove-double-neg 48.8%

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

       8. distribute-neg-frac 48.8%

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

   14. Applied egg-rr 48.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 50.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;\frac{y \cdot x}{-t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.9e+61)
   x
   (if (<= t -2.8e-52)
     (/ (* y x) (- t))
     (if (<= t -1.2e-107) x (if (<= t 2.1e-46) (/ x (/ (- t) y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.9e+61) {
		tmp = x;
	} else if (t <= -2.8e-52) {
		tmp = (y * x) / -t;
	} else if (t <= -1.2e-107) {
		tmp = x;
	} else if (t <= 2.1e-46) {
		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 (t <= (-4.9d+61)) then
        tmp = x
    else if (t <= (-2.8d-52)) then
        tmp = (y * x) / -t
    else if (t <= (-1.2d-107)) then
        tmp = x
    else if (t <= 2.1d-46) 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 (t <= -4.9e+61) {
		tmp = x;
	} else if (t <= -2.8e-52) {
		tmp = (y * x) / -t;
	} else if (t <= -1.2e-107) {
		tmp = x;
	} else if (t <= 2.1e-46) {
		tmp = x / (-t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.9e+61:
		tmp = x
	elif t <= -2.8e-52:
		tmp = (y * x) / -t
	elif t <= -1.2e-107:
		tmp = x
	elif t <= 2.1e-46:
		tmp = x / (-t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.9e+61)
		tmp = x;
	elseif (t <= -2.8e-52)
		tmp = Float64(Float64(y * x) / Float64(-t));
	elseif (t <= -1.2e-107)
		tmp = x;
	elseif (t <= 2.1e-46)
		tmp = Float64(x / Float64(Float64(-t) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.9e+61)
		tmp = x;
	elseif (t <= -2.8e-52)
		tmp = (y * x) / -t;
	elseif (t <= -1.2e-107)
		tmp = x;
	elseif (t <= 2.1e-46)
		tmp = x / (-t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.9e+61], x, If[LessEqual[t, -2.8e-52], N[(N[(y * x), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[t, -1.2e-107], x, If[LessEqual[t, 2.1e-46], N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.90000000000000025e61 or -2.79999999999999995e-52 < t < -1.19999999999999997e-107 or 2.09999999999999987e-46 < t

   1. Initial program 87.4%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in y around 0 66.0%

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

   if -4.90000000000000025e61 < t < -2.79999999999999995e-52

   1. Initial program 99.9%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. unsub-neg 40.5%

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

   6. Simplified 40.5%

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

   7. Taylor expanded in y around inf 28.7%

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

      1. mul-1-neg 28.7%

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

      2. distribute-frac-neg 28.7%

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

   9. Simplified 28.7%

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

       1. frac-2neg 28.7%

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

       2. remove-double-neg 28.7%

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

       3. associate-*r/ 32.4%

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

       4. *-commutative 32.4%

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

   11. Applied egg-rr 32.4%

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

   if -1.19999999999999997e-107 < t < 2.09999999999999987e-46

   1. Initial program 98.7%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in y around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. distribute-frac-neg 48.7%

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

   9. Simplified 48.7%

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

   10. Taylor expanded in x around 0 42.7%

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

       1. associate-*r/ 42.7%

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

       2. *-commutative 42.7%

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

       3. neg-mul-1 42.7%

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

       4. distribute-rgt-neg-out 42.7%

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

       5. associate-*r/ 38.3%

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

   12. Simplified 38.3%

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

       1. *-commutative 38.3%

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

       2. distribute-frac-neg 38.3%

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

       3. distribute-lft-neg-in 38.3%

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

       4. associate-/r/ 48.8%

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

       5. frac-2neg 48.8%

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

       6. distribute-neg-frac 48.8%

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

       7. remove-double-neg 48.8%

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

       8. distribute-neg-frac 48.8%

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

   14. Applied egg-rr 48.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;\frac{y \cdot x}{-t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-77} \lor \neg \left(x \leq 5.4 \cdot 10^{+78}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.9e-77) (not (<= x 5.4e+78)))
   (* x (- 1.0 (/ y t)))
   (+ x (* (/ y t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.9e-77) || !(x <= 5.4e+78)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	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 ((x <= (-2.9d-77)) .or. (.not. (x <= 5.4d+78))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + ((y / t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.9e-77) || !(x <= 5.4e+78)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.9e-77) or not (x <= 5.4e+78):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.9e-77) || !(x <= 5.4e+78))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.9e-77) || ~((x <= 5.4e+78)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.9e-77], N[Not[LessEqual[x, 5.4e+78]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8999999999999999e-77 or 5.40000000000000009e78 < x

   1. Initial program 91.4%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

   6. Simplified 89.4%

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

   if -2.8999999999999999e-77 < x < 5.40000000000000009e78

   1. Initial program 93.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 86.3%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   6. Simplified 90.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-77} \lor \neg \left(x \leq 5.4 \cdot 10^{+78}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]

Alternative 6: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.05e-75)
   (* x (- 1.0 (/ y t)))
   (if (<= x 5.5e+78) (+ x (* (/ y t) z)) (- x (/ x (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.05e-75) {
		tmp = x * (1.0 - (y / t));
	} else if (x <= 5.5e+78) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (x / (t / y));
	}
	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 (x <= (-3.05d-75)) then
        tmp = x * (1.0d0 - (y / t))
    else if (x <= 5.5d+78) then
        tmp = x + ((y / t) * z)
    else
        tmp = x - (x / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.05e-75) {
		tmp = x * (1.0 - (y / t));
	} else if (x <= 5.5e+78) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (x / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.05e-75:
		tmp = x * (1.0 - (y / t))
	elif x <= 5.5e+78:
		tmp = x + ((y / t) * z)
	else:
		tmp = x - (x / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.05e-75)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (x <= 5.5e+78)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x - Float64(x / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.05e-75)
		tmp = x * (1.0 - (y / t));
	elseif (x <= 5.5e+78)
		tmp = x + ((y / t) * z);
	else
		tmp = x - (x / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.05e-75], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+78], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.05000000000000021e-75

   1. Initial program 92.7%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 87.8%

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

      1. mul-1-neg 87.8%

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

      2. unsub-neg 87.8%

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

   6. Simplified 87.8%

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

   if -3.05000000000000021e-75 < x < 5.4999999999999997e78

   1. Initial program 93.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around inf 86.3%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   6. Simplified 90.0%

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

   if 5.4999999999999997e78 < x

   1. Initial program 89.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. associate-/l* 92.3%

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

      3. distribute-neg-frac 92.3%

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

   6. Simplified 92.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \end{array} \]

Alternative 7: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-107) x (if (<= t 3.2e-46) (* (/ y t) (- x)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-107) {
		tmp = x;
	} else if (t <= 3.2e-46) {
		tmp = (y / t) * -x;
	} 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 (t <= (-4.2d-107)) then
        tmp = x
    else if (t <= 3.2d-46) then
        tmp = (y / t) * -x
    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 (t <= -4.2e-107) {
		tmp = x;
	} else if (t <= 3.2e-46) {
		tmp = (y / t) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.2e-107:
		tmp = x
	elif t <= 3.2e-46:
		tmp = (y / t) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e-107)
		tmp = x;
	elseif (t <= 3.2e-46)
		tmp = Float64(Float64(y / t) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.2e-107)
		tmp = x;
	elseif (t <= 3.2e-46)
		tmp = (y / t) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e-107], x, If[LessEqual[t, 3.2e-46], N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1999999999999998e-107 or 3.1999999999999999e-46 < t

   1. Initial program 89.3%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around 0 58.5%

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

   if -4.1999999999999998e-107 < t < 3.1999999999999999e-46

   1. Initial program 98.7%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in y around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. distribute-frac-neg 48.7%

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

   9. Simplified 48.7%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. associate-*l/ 98.1%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 9: 66.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{y}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ y t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (y / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (y / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (y / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(y / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (y / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.7%

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

   1. associate-*l/ 98.1%

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

3. Simplified 98.1%

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

4. Taylor expanded in x around inf 66.2%

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

   1. mul-1-neg 66.2%

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

   2. unsub-neg 66.2%

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

6. Simplified 66.2%

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

7. Final simplification 66.2%

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

Alternative 10: 39.4% 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 92.7%

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

   1. associate-*l/ 98.1%

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

3. Simplified 98.1%

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

4. Taylor expanded in y around 0 39.9%

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

5. Final simplification 39.9%

   \[\leadsto x \]

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 2023336 
(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)))