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

Percentage Accurate: 93.4% → 97.4%

Time: 10.8s

Alternatives: 9

Speedup: 1.0×

• 25.3% 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: 93.4% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. *-commutative 93.6%

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

   2. associate-/l* 98.1%

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

3. Simplified 98.1%

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

5. Final simplification 98.1%

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

Alternative 2: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+197}:\\ \;\;\;\;\frac{y}{\frac{a}{-t}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+128}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+287}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+197)
   (/ y (/ a (- t)))
   (if (<= t 1.56e+128)
     (+ x (/ y (/ a z)))
     (if (<= t 1.1e+287) (* t (/ y (- a))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+197) {
		tmp = y / (a / -t);
	} else if (t <= 1.56e+128) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.1e+287) {
		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 (t <= (-4.5d+197)) then
        tmp = y / (a / -t)
    else if (t <= 1.56d+128) then
        tmp = x + (y / (a / z))
    else if (t <= 1.1d+287) 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 (t <= -4.5e+197) {
		tmp = y / (a / -t);
	} else if (t <= 1.56e+128) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.1e+287) {
		tmp = t * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+197:
		tmp = y / (a / -t)
	elif t <= 1.56e+128:
		tmp = x + (y / (a / z))
	elif t <= 1.1e+287:
		tmp = t * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+197)
		tmp = Float64(y / Float64(a / Float64(-t)));
	elseif (t <= 1.56e+128)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.1e+287)
		tmp = Float64(t * Float64(y / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e+197)
		tmp = y / (a / -t);
	elseif (t <= 1.56e+128)
		tmp = x + (y / (a / z));
	elseif (t <= 1.1e+287)
		tmp = t * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+197], N[(y / N[(a / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.56e+128], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+287], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.5000000000000003e197

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. distribute-lft-neg-out 89.3%

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

      3. *-commutative 89.3%

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

   5. Simplified 89.3%

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

      1. div-inv 89.2%

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

      2. add-sqr-sqrt 89.0%

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

      3. sqrt-unprod 39.6%

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

      4. sqr-neg 39.6%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 15.9%

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

      7. remove-double-neg 15.9%

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

      8. distribute-rgt-neg-out 15.9%

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

      9. cancel-sign-sub-inv 15.9%

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

      10. div-inv 15.9%

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

      11. *-un-lft-identity 15.9%

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

      12. times-frac 12.0%

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

      13. /-rgt-identity 12.0%

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

      14. add-sqr-sqrt 12.0%

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

      15. sqrt-unprod 0.4%

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

      16. sqr-neg 0.4%

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

      17. sqrt-unprod 0.0%

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

      18. add-sqr-sqrt 94.2%

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

   7. Applied egg-rr 94.2%

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

   8. Taylor expanded in x around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. *-commutative 72.6%

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

      3. neg-mul-1 72.6%

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

      4. distribute-rgt-neg-in 72.6%

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

      5. associate-/l* 82.9%

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

   10. Simplified 82.9%

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

   if -4.5000000000000003e197 < t < 1.55999999999999992e128

   1. Initial program 94.2%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around inf 81.5%

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

   if 1.55999999999999992e128 < t < 1.10000000000000002e287

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-lft-neg-out 82.6%

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

      3. *-commutative 82.6%

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

   5. Simplified 82.6%

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

      1. div-inv 82.6%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 6.7%

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

      4. sqr-neg 6.7%

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

      5. sqrt-unprod 24.8%

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

      6. add-sqr-sqrt 24.8%

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

      7. remove-double-neg 24.8%

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

      8. distribute-rgt-neg-out 24.8%

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

      9. cancel-sign-sub-inv 24.8%

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

      10. div-inv 24.8%

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

      11. *-un-lft-identity 24.8%

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

      12. times-frac 27.6%

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

      13. /-rgt-identity 27.6%

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

      14. add-sqr-sqrt 0.0%

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

      15. sqrt-unprod 59.5%

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

      16. sqr-neg 59.5%

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

      17. sqrt-unprod 88.4%

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

      18. add-sqr-sqrt 88.4%

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

   7. Applied egg-rr 88.4%

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

   8. Taylor expanded in x around 0 62.0%

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

      1. associate-*r/ 62.0%

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

      2. *-commutative 62.0%

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

      3. neg-mul-1 62.0%

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

      4. distribute-rgt-neg-in 62.0%

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

      5. associate-/l* 64.8%

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

   10. Simplified 64.8%

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

       1. frac-2neg 64.8%

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

       2. remove-double-neg 64.8%

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

       3. associate-/r/ 67.5%

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

   12. Applied egg-rr 67.5%

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

   if 1.10000000000000002e287 < t

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

      3. fma-udef 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+197}:\\ \;\;\;\;\frac{y}{\frac{a}{-t}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+128}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+287}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+197}:\\ \;\;\;\;\frac{y}{\frac{a}{-t}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+287}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.9e+197)
   (/ y (/ a (- t)))
   (if (<= t 1.75e+133)
     (+ x (/ z (/ a y)))
     (if (<= t 1.1e+287) (* t (/ y (- a))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.9e+197) {
		tmp = y / (a / -t);
	} else if (t <= 1.75e+133) {
		tmp = x + (z / (a / y));
	} else if (t <= 1.1e+287) {
		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 (t <= (-5.9d+197)) then
        tmp = y / (a / -t)
    else if (t <= 1.75d+133) then
        tmp = x + (z / (a / y))
    else if (t <= 1.1d+287) 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 (t <= -5.9e+197) {
		tmp = y / (a / -t);
	} else if (t <= 1.75e+133) {
		tmp = x + (z / (a / y));
	} else if (t <= 1.1e+287) {
		tmp = t * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.9e+197:
		tmp = y / (a / -t)
	elif t <= 1.75e+133:
		tmp = x + (z / (a / y))
	elif t <= 1.1e+287:
		tmp = t * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.9e+197)
		tmp = Float64(y / Float64(a / Float64(-t)));
	elseif (t <= 1.75e+133)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (t <= 1.1e+287)
		tmp = Float64(t * Float64(y / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.9e+197)
		tmp = y / (a / -t);
	elseif (t <= 1.75e+133)
		tmp = x + (z / (a / y));
	elseif (t <= 1.1e+287)
		tmp = t * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.9e+197], N[(y / N[(a / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+133], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+287], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.89999999999999988e197

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. distribute-lft-neg-out 89.3%

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

      3. *-commutative 89.3%

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

   5. Simplified 89.3%

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

      1. div-inv 89.2%

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

      2. add-sqr-sqrt 89.0%

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

      3. sqrt-unprod 39.6%

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

      4. sqr-neg 39.6%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 15.9%

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

      7. remove-double-neg 15.9%

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

      8. distribute-rgt-neg-out 15.9%

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

      9. cancel-sign-sub-inv 15.9%

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

      10. div-inv 15.9%

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

      11. *-un-lft-identity 15.9%

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

      12. times-frac 12.0%

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

      13. /-rgt-identity 12.0%

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

      14. add-sqr-sqrt 12.0%

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

      15. sqrt-unprod 0.4%

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

      16. sqr-neg 0.4%

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

      17. sqrt-unprod 0.0%

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

      18. add-sqr-sqrt 94.2%

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

   7. Applied egg-rr 94.2%

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

   8. Taylor expanded in x around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. *-commutative 72.6%

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

      3. neg-mul-1 72.6%

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

      4. distribute-rgt-neg-in 72.6%

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

      5. associate-/l* 82.9%

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

   10. Simplified 82.9%

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

   if -5.89999999999999988e197 < t < 1.7499999999999999e133

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*r/ 96.1%

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

      3. fma-udef 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. associate-*r/ 81.5%

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

   7. Simplified 81.5%

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

      1. associate-*r/ 79.6%

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

      2. associate-*l/ 84.3%

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

      3. clear-num 84.3%

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

      4. associate-*l/ 84.3%

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

      5. *-un-lft-identity 84.3%

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

   9. Applied egg-rr 84.3%

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

   if 1.7499999999999999e133 < t < 1.10000000000000002e287

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-lft-neg-out 82.6%

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

      3. *-commutative 82.6%

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

   5. Simplified 82.6%

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

      1. div-inv 82.6%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 6.7%

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

      4. sqr-neg 6.7%

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

      5. sqrt-unprod 24.8%

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

      6. add-sqr-sqrt 24.8%

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

      7. remove-double-neg 24.8%

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

      8. distribute-rgt-neg-out 24.8%

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

      9. cancel-sign-sub-inv 24.8%

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

      10. div-inv 24.8%

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

      11. *-un-lft-identity 24.8%

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

      12. times-frac 27.6%

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

      13. /-rgt-identity 27.6%

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

      14. add-sqr-sqrt 0.0%

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

      15. sqrt-unprod 59.5%

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

      16. sqr-neg 59.5%

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

      17. sqrt-unprod 88.4%

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

      18. add-sqr-sqrt 88.4%

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

   7. Applied egg-rr 88.4%

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

   8. Taylor expanded in x around 0 62.0%

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

      1. associate-*r/ 62.0%

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

      2. *-commutative 62.0%

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

      3. neg-mul-1 62.0%

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

      4. distribute-rgt-neg-in 62.0%

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

      5. associate-/l* 64.8%

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

   10. Simplified 64.8%

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

       1. frac-2neg 64.8%

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

       2. remove-double-neg 64.8%

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

       3. associate-/r/ 67.5%

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

   12. Applied egg-rr 67.5%

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

   if 1.10000000000000002e287 < t

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

      3. fma-udef 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+197}:\\ \;\;\;\;\frac{y}{\frac{a}{-t}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+287}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+37} \lor \neg \left(z \leq 1.08 \cdot 10^{-73}\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+37) (not (<= z 1.08e-73)))
   (+ x (/ z (/ a y)))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+37) || !(z <= 1.08e-73)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.65d+37)) .or. (.not. (z <= 1.08d-73))) then
        tmp = x + (z / (a / y))
    else
        tmp = x - (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+37) || !(z <= 1.08e-73)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+37) or not (z <= 1.08e-73):
		tmp = x + (z / (a / y))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+37) || !(z <= 1.08e-73))
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e+37) || ~((z <= 1.08e-73)))
		tmp = x + (z / (a / y));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+37], N[Not[LessEqual[z, 1.08e-73]], $MachinePrecision]], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e37 or 1.08000000000000007e-73 < z

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-*r/ 95.6%

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

      3. fma-udef 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 82.5%

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

      1. +-commutative 82.5%

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

      2. associate-*r/ 85.3%

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

   7. Simplified 85.3%

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

      1. associate-*r/ 82.5%

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

      2. associate-*l/ 88.1%

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

      3. clear-num 88.1%

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

      4. associate-*l/ 88.2%

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

      5. *-un-lft-identity 88.2%

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

   9. Applied egg-rr 88.2%

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

   if -1.65e37 < z < 1.08000000000000007e-73

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 89.4%

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

      1. mul-1-neg 89.4%

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

      2. distribute-lft-neg-out 89.4%

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

      3. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in x around 0 89.4%

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

      1. mul-1-neg 89.4%

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

      2. associate-*r/ 91.6%

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

      3. distribute-lft-neg-in 91.6%

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

      4. cancel-sign-sub-inv 91.6%

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

   8. Simplified 91.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+37} \lor \neg \left(z \leq 1.08 \cdot 10^{-73}\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+37} \lor \neg \left(z \leq 3.15 \cdot 10^{-71}\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+37) (not (<= z 3.15e-71)))
   (+ x (/ z (/ a y)))
   (- x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+37) || !(z <= 3.15e-71)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9d+37)) .or. (.not. (z <= 3.15d-71))) then
        tmp = x + (z / (a / y))
    else
        tmp = x - (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+37) || !(z <= 3.15e-71)) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+37) or not (z <= 3.15e-71):
		tmp = x + (z / (a / y))
	else:
		tmp = x - (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+37) || !(z <= 3.15e-71))
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x - Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+37) || ~((z <= 3.15e-71)))
		tmp = x + (z / (a / y));
	else
		tmp = x - (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+37], N[Not[LessEqual[z, 3.15e-71]], $MachinePrecision]], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999923e37 or 3.1500000000000002e-71 < z

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-*r/ 95.6%

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

      3. fma-udef 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 82.5%

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

      1. +-commutative 82.5%

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

      2. associate-*r/ 85.3%

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

   7. Simplified 85.3%

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

      1. associate-*r/ 82.5%

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

      2. associate-*l/ 88.1%

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

      3. clear-num 88.1%

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

      4. associate-*l/ 88.2%

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

      5. *-un-lft-identity 88.2%

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

   9. Applied egg-rr 88.2%

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

   if -8.99999999999999923e37 < z < 3.1500000000000002e-71

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 89.4%

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

      1. mul-1-neg 89.4%

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

      2. distribute-lft-neg-out 89.4%

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

      3. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in x around 0 89.4%

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

      1. mul-1-neg 89.4%

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

      2. associate-*r/ 91.6%

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

      3. distribute-lft-neg-in 91.6%

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

      4. cancel-sign-sub-inv 91.6%

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

   8. Simplified 91.6%

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

      1. clear-num 91.6%

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

      2. un-div-inv 91.7%

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

   10. Applied egg-rr 91.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+37} \lor \neg \left(z \leq 3.15 \cdot 10^{-71}\right):\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e-93) x (if (<= a 2.8e-32) (* y (/ (- t) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-93) {
		tmp = x;
	} else if (a <= 2.8e-32) {
		tmp = y * (-t / 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 (a <= (-2.8d-93)) then
        tmp = x
    else if (a <= 2.8d-32) then
        tmp = y * (-t / 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 (a <= -2.8e-93) {
		tmp = x;
	} else if (a <= 2.8e-32) {
		tmp = y * (-t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e-93:
		tmp = x
	elif a <= 2.8e-32:
		tmp = y * (-t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e-93)
		tmp = x;
	elseif (a <= 2.8e-32)
		tmp = Float64(y * Float64(Float64(-t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e-93)
		tmp = x;
	elseif (a <= 2.8e-32)
		tmp = y * (-t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e-93], x, If[LessEqual[a, 2.8e-32], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.79999999999999998e-93 or 2.7999999999999999e-32 < a

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. associate-*r/ 98.7%

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

      3. fma-udef 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 59.2%

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

   if -2.79999999999999998e-93 < a < 2.7999999999999999e-32

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-lft-neg-out 61.4%

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

      3. *-commutative 61.4%

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

   5. Simplified 61.4%

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

      1. div-inv 61.4%

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

      2. add-sqr-sqrt 27.0%

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

      3. sqrt-unprod 34.5%

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

      4. sqr-neg 34.5%

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

      5. sqrt-unprod 12.7%

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

      6. add-sqr-sqrt 16.6%

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

      7. remove-double-neg 16.6%

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

      8. distribute-rgt-neg-out 16.6%

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

      9. cancel-sign-sub-inv 16.6%

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

      10. div-inv 16.6%

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

      11. *-un-lft-identity 16.6%

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

      12. times-frac 16.5%

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

      13. /-rgt-identity 16.5%

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

      14. add-sqr-sqrt 3.8%

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

      15. sqrt-unprod 36.2%

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

      16. sqr-neg 36.2%

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

      17. sqrt-unprod 33.3%

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

      18. add-sqr-sqrt 60.5%

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

   7. Applied egg-rr 60.5%

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

   8. Taylor expanded in x around 0 50.5%

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

      1. associate-*r/ 50.5%

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

      2. *-commutative 50.5%

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

      3. neg-mul-1 50.5%

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

      4. distribute-rgt-neg-in 50.5%

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

      5. associate-*r/ 49.4%

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

   10. Simplified 49.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.55 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.55e-93) x (if (<= a 4.8e-67) (* t (/ y (- a))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.55e-93) {
		tmp = x;
	} else if (a <= 4.8e-67) {
		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 (a <= (-3.55d-93)) then
        tmp = x
    else if (a <= 4.8d-67) 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 (a <= -3.55e-93) {
		tmp = x;
	} else if (a <= 4.8e-67) {
		tmp = t * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.55e-93:
		tmp = x
	elif a <= 4.8e-67:
		tmp = t * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.55e-93)
		tmp = x;
	elseif (a <= 4.8e-67)
		tmp = Float64(t * Float64(y / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.55e-93)
		tmp = x;
	elseif (a <= 4.8e-67)
		tmp = t * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.55e-93], x, If[LessEqual[a, 4.8e-67], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.55e-93 or 4.8e-67 < a

   1. Initial program 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-*r/ 98.7%

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

      3. fma-udef 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 57.7%

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

   if -3.55e-93 < a < 4.8e-67

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. distribute-lft-neg-out 62.4%

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

      3. *-commutative 62.4%

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

   5. Simplified 62.4%

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

      1. div-inv 62.4%

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

      2. add-sqr-sqrt 29.7%

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

      3. sqrt-unprod 35.3%

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

      4. sqr-neg 35.3%

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

      5. sqrt-unprod 11.4%

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

      6. add-sqr-sqrt 15.6%

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

      7. remove-double-neg 15.6%

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

      8. distribute-rgt-neg-out 15.6%

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

      9. cancel-sign-sub-inv 15.6%

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

      10. div-inv 15.6%

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

      11. *-un-lft-identity 15.6%

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

      12. times-frac 15.6%

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

      13. /-rgt-identity 15.6%

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

      14. add-sqr-sqrt 4.2%

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

      15. sqrt-unprod 34.8%

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

      16. sqr-neg 34.8%

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

      17. sqrt-unprod 31.5%

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

      18. add-sqr-sqrt 61.4%

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

   7. Applied egg-rr 61.4%

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

   8. Taylor expanded in x around 0 52.8%

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

      1. associate-*r/ 52.8%

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

      2. *-commutative 52.8%

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

      3. neg-mul-1 52.8%

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

      4. distribute-rgt-neg-in 52.8%

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

      5. associate-/l* 51.6%

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

   10. Simplified 51.6%

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

       1. frac-2neg 51.6%

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

       2. remove-double-neg 51.6%

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

       3. associate-/r/ 58.6%

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

   12. Applied egg-rr 58.6%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.55 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 9: 39.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. +-commutative 93.6%

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

   2. associate-*r/ 96.1%

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

   3. fma-udef 96.1%

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

3. Simplified 96.1%

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

5. Taylor expanded in y around 0 43.3%

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

6. Final simplification 43.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.1% 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 2024020 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

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

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