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

Percentage Accurate: 93.3% → 97.4%

Time: 7.7s

Alternatives: 9

Speedup: 1.0×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 1.0× speedup

Math

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

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 90.3%

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

   1. associate-*l/ 97.7%

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

3. Simplified 97.7%

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

   1. *-commutative 97.7%

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

   2. clear-num 96.8%

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

   3. un-div-inv 97.7%

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

5. Applied egg-rr 97.7%

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

6. Final simplification 97.7%

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

Alternative 2: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -100 \lor \neg \left(t \leq 3.5 \cdot 10^{+32}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -100.0) (not (<= t 3.5e+32)))
   (- x (* t (/ y a)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -100.0) || !(t <= 3.5e+32)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (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 ((t <= (-100.0d0)) .or. (.not. (t <= 3.5d+32))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z / (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 ((t <= -100.0) || !(t <= 3.5e+32)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -100.0) or not (t <= 3.5e+32):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -100.0) || !(t <= 3.5e+32))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -100.0) || ~((t <= 3.5e+32)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -100.0], N[Not[LessEqual[t, 3.5e+32]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -100 or 3.5000000000000001e32 < t

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-*r/ 89.7%

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

      3. fma-def 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. unsub-neg 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-*r/ 86.7%

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

   6. Simplified 86.7%

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

   if -100 < t < 3.5000000000000001e32

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-*r/ 94.4%

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

      3. fma-def 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around 0 88.9%

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

      1. associate-*l/ 94.4%

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

      2. *-commutative 94.4%

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

   6. Simplified 94.4%

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

      1. clear-num 93.6%

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

      2. un-div-inv 95.2%

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

   8. Applied egg-rr 95.2%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -100 \lor \neg \left(t \leq 3.5 \cdot 10^{+32}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+162)
   (* t (/ (- y) a))
   (if (<= t 3.5e+114) (+ x (* y (/ z a))) (* y (/ t (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+162) {
		tmp = t * (-y / a);
	} else if (t <= 3.5e+114) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4d+162)) then
        tmp = t * (-y / a)
    else if (t <= 3.5d+114) then
        tmp = x + (y * (z / a))
    else
        tmp = y * (t / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+162) {
		tmp = t * (-y / a);
	} else if (t <= 3.5e+114) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+162:
		tmp = t * (-y / a)
	elif t <= 3.5e+114:
		tmp = x + (y * (z / a))
	else:
		tmp = y * (t / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+162)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (t <= 3.5e+114)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y * Float64(t / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+162)
		tmp = t * (-y / a);
	elseif (t <= 3.5e+114)
		tmp = x + (y * (z / a));
	else
		tmp = y * (t / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+162], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+114], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9999999999999998e162

   1. Initial program 84.7%

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

      1. +-commutative 84.7%

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

      2. associate-*r/ 84.9%

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

      3. fma-def 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. mul-1-neg 81.8%

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

      3. unsub-neg 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-*r/ 96.0%

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

   6. Simplified 96.0%

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

      1. clear-num 93.8%

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

      2. div-inv 93.9%

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

   8. Applied egg-rr 93.9%

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

   9. Taylor expanded in x around 0 60.3%

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

       1. associate-/l* 57.3%

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

       2. associate-*r/ 57.3%

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

       3. neg-mul-1 57.3%

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

       4. associate-/r/ 71.2%

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

       5. *-commutative 71.2%

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

       6. distribute-frac-neg 71.2%

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

   11. Simplified 71.2%

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

   if -3.9999999999999998e162 < t < 3.5000000000000001e114

   1. Initial program 91.5%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 97.5%

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

      3. un-div-inv 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in z around inf 80.0%

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

      1. associate-*r/ 82.6%

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

   8. Simplified 82.6%

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

   if 3.5000000000000001e114 < t

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-*r/ 95.5%

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

      3. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-*r/ 85.4%

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

   6. Simplified 85.4%

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

      1. clear-num 83.6%

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

      2. div-inv 83.6%

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

   8. Applied egg-rr 83.6%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. associate-*r/ 66.3%

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

       2. associate-*l/ 66.2%

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

       3. metadata-eval 66.2%

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

       4. distribute-neg-frac 66.2%

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

       5. associate-*r* 67.9%

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

       6. distribute-neg-frac 67.9%

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

       7. metadata-eval 67.9%

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

       8. metadata-eval 67.9%

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

       9. associate-/r* 67.9%

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

       10. neg-mul-1 67.9%

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

       11. associate-/r/ 66.2%

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

       12. *-commutative 66.2%

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

       13. associate-*r/ 66.2%

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

       14. *-rgt-identity 66.2%

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

       15. associate-/r/ 74.2%

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

       16. *-commutative 74.2%

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

   11. Simplified 74.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \]

Alternative 4: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+116}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e+161)
   (* t (/ (- y) a))
   (if (<= t 1.25e+116) (+ x (/ y (/ a z))) (* y (/ t (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+161) {
		tmp = t * (-y / a);
	} else if (t <= 1.25e+116) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.9d+161)) then
        tmp = t * (-y / a)
    else if (t <= 1.25d+116) then
        tmp = x + (y / (a / z))
    else
        tmp = y * (t / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+161) {
		tmp = t * (-y / a);
	} else if (t <= 1.25e+116) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e+161:
		tmp = t * (-y / a)
	elif t <= 1.25e+116:
		tmp = x + (y / (a / z))
	else:
		tmp = y * (t / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e+161)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (t <= 1.25e+116)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y * Float64(t / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e+161)
		tmp = t * (-y / a);
	elseif (t <= 1.25e+116)
		tmp = x + (y / (a / z));
	else
		tmp = y * (t / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e+161], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+116], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.90000000000000016e161

   1. Initial program 84.7%

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

      1. +-commutative 84.7%

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

      2. associate-*r/ 84.9%

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

      3. fma-def 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. mul-1-neg 81.8%

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

      3. unsub-neg 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-*r/ 96.0%

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

   6. Simplified 96.0%

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

      1. clear-num 93.8%

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

      2. div-inv 93.9%

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

   8. Applied egg-rr 93.9%

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

   9. Taylor expanded in x around 0 60.3%

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

       1. associate-/l* 57.3%

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

       2. associate-*r/ 57.3%

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

       3. neg-mul-1 57.3%

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

       4. associate-/r/ 71.2%

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

       5. *-commutative 71.2%

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

       6. distribute-frac-neg 71.2%

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

   11. Simplified 71.2%

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

   if -2.90000000000000016e161 < t < 1.25000000000000006e116

   1. Initial program 91.5%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 83.0%

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

   if 1.25000000000000006e116 < t

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-*r/ 95.5%

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

      3. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-*r/ 85.4%

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

   6. Simplified 85.4%

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

      1. clear-num 83.6%

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

      2. div-inv 83.6%

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

   8. Applied egg-rr 83.6%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. associate-*r/ 66.3%

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

       2. associate-*l/ 66.2%

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

       3. metadata-eval 66.2%

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

       4. distribute-neg-frac 66.2%

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

       5. associate-*r* 67.9%

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

       6. distribute-neg-frac 67.9%

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

       7. metadata-eval 67.9%

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

       8. metadata-eval 67.9%

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

       9. associate-/r* 67.9%

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

       10. neg-mul-1 67.9%

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

       11. associate-/r/ 66.2%

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

       12. *-commutative 66.2%

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

       13. associate-*r/ 66.2%

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

       14. *-rgt-identity 66.2%

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

       15. associate-/r/ 74.2%

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

       16. *-commutative 74.2%

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

   11. Simplified 74.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+116}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \]

Alternative 5: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+115}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+162)
   (* t (/ (- y) a))
   (if (<= t 1.65e+115) (+ x (* z (/ y a))) (* y (/ t (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+162) {
		tmp = t * (-y / a);
	} else if (t <= 1.65e+115) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.6d+162)) then
        tmp = t * (-y / a)
    else if (t <= 1.65d+115) then
        tmp = x + (z * (y / a))
    else
        tmp = y * (t / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+162) {
		tmp = t * (-y / a);
	} else if (t <= 1.65e+115) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+162:
		tmp = t * (-y / a)
	elif t <= 1.65e+115:
		tmp = x + (z * (y / a))
	else:
		tmp = y * (t / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+162)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (t <= 1.65e+115)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y * Float64(t / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+162)
		tmp = t * (-y / a);
	elseif (t <= 1.65e+115)
		tmp = x + (z * (y / a));
	else
		tmp = y * (t / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+162], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+115], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999994e162

   1. Initial program 84.7%

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

      1. +-commutative 84.7%

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

      2. associate-*r/ 84.9%

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

      3. fma-def 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. mul-1-neg 81.8%

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

      3. unsub-neg 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-*r/ 96.0%

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

   6. Simplified 96.0%

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

      1. clear-num 93.8%

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

      2. div-inv 93.9%

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

   8. Applied egg-rr 93.9%

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

   9. Taylor expanded in x around 0 60.3%

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

       1. associate-/l* 57.3%

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

       2. associate-*r/ 57.3%

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

       3. neg-mul-1 57.3%

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

       4. associate-/r/ 71.2%

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

       5. *-commutative 71.2%

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

       6. distribute-frac-neg 71.2%

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

   11. Simplified 71.2%

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

   if -3.59999999999999994e162 < t < 1.65000000000000003e115

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-*r/ 92.9%

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

      3. fma-def 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around 0 80.0%

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

      1. associate-*l/ 85.3%

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

      2. *-commutative 85.3%

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

   6. Simplified 85.3%

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

   if 1.65000000000000003e115 < t

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-*r/ 95.5%

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

      3. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-*r/ 85.4%

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

   6. Simplified 85.4%

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

      1. clear-num 83.6%

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

      2. div-inv 83.6%

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

   8. Applied egg-rr 83.6%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. associate-*r/ 66.3%

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

       2. associate-*l/ 66.2%

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

       3. metadata-eval 66.2%

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

       4. distribute-neg-frac 66.2%

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

       5. associate-*r* 67.9%

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

       6. distribute-neg-frac 67.9%

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

       7. metadata-eval 67.9%

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

       8. metadata-eval 67.9%

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

       9. associate-/r* 67.9%

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

       10. neg-mul-1 67.9%

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

       11. associate-/r/ 66.2%

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

       12. *-commutative 66.2%

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

       13. associate-*r/ 66.2%

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

       14. *-rgt-identity 66.2%

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

       15. associate-/r/ 74.2%

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

       16. *-commutative 74.2%

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

   11. Simplified 74.2%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+115}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \]

Alternative 6: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+162)
   (* t (/ (- y) a))
   (if (<= t 3.5e+114) (+ x (/ z (/ a y))) (* y (/ t (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+162) {
		tmp = t * (-y / a);
	} else if (t <= 3.5e+114) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3d+162)) then
        tmp = t * (-y / a)
    else if (t <= 3.5d+114) then
        tmp = x + (z / (a / y))
    else
        tmp = y * (t / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+162) {
		tmp = t * (-y / a);
	} else if (t <= 3.5e+114) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e+162:
		tmp = t * (-y / a)
	elif t <= 3.5e+114:
		tmp = x + (z / (a / y))
	else:
		tmp = y * (t / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+162)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (t <= 3.5e+114)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(y * Float64(t / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e+162)
		tmp = t * (-y / a);
	elseif (t <= 3.5e+114)
		tmp = x + (z / (a / y));
	else
		tmp = y * (t / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+162], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+114], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9999999999999998e162

   1. Initial program 84.7%

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

      1. +-commutative 84.7%

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

      2. associate-*r/ 84.9%

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

      3. fma-def 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. mul-1-neg 81.8%

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

      3. unsub-neg 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-*r/ 96.0%

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

   6. Simplified 96.0%

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

      1. clear-num 93.8%

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

      2. div-inv 93.9%

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

   8. Applied egg-rr 93.9%

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

   9. Taylor expanded in x around 0 60.3%

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

       1. associate-/l* 57.3%

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

       2. associate-*r/ 57.3%

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

       3. neg-mul-1 57.3%

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

       4. associate-/r/ 71.2%

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

       5. *-commutative 71.2%

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

       6. distribute-frac-neg 71.2%

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

   11. Simplified 71.2%

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

   if -2.9999999999999998e162 < t < 3.5000000000000001e114

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-*r/ 92.9%

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

      3. fma-def 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around 0 80.0%

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

      1. associate-*l/ 85.3%

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

      2. *-commutative 85.3%

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

   6. Simplified 85.3%

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

      1. clear-num 84.9%

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

      2. un-div-inv 85.9%

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

   8. Applied egg-rr 85.9%

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

   if 3.5000000000000001e114 < t

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-*r/ 95.5%

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

      3. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-*r/ 85.4%

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

   6. Simplified 85.4%

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

      1. clear-num 83.6%

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

      2. div-inv 83.6%

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

   8. Applied egg-rr 83.6%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. associate-*r/ 66.3%

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

       2. associate-*l/ 66.2%

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

       3. metadata-eval 66.2%

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

       4. distribute-neg-frac 66.2%

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

       5. associate-*r* 67.9%

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

       6. distribute-neg-frac 67.9%

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

       7. metadata-eval 67.9%

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

       8. metadata-eval 67.9%

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

       9. associate-/r* 67.9%

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

       10. neg-mul-1 67.9%

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

       11. associate-/r/ 66.2%

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

       12. *-commutative 66.2%

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

       13. associate-*r/ 66.2%

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

       14. *-rgt-identity 66.2%

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

       15. associate-/r/ 74.2%

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

       16. *-commutative 74.2%

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

   11. Simplified 74.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \]

Alternative 7: 50.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.1e-94) x (if (<= a 2.2e-32) (* t (/ (- y) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e-94) {
		tmp = x;
	} else if (a <= 2.2e-32) {
		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 <= (-4.1d-94)) then
        tmp = x
    else if (a <= 2.2d-32) 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 <= -4.1e-94) {
		tmp = x;
	} else if (a <= 2.2e-32) {
		tmp = t * (-y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.1e-94:
		tmp = x
	elif a <= 2.2e-32:
		tmp = t * (-y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.1e-94)
		tmp = x;
	elseif (a <= 2.2e-32)
		tmp = Float64(t * Float64(Float64(-y) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.1e-94)
		tmp = x;
	elseif (a <= 2.2e-32)
		tmp = t * (-y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.1e-94], x, If[LessEqual[a, 2.2e-32], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.10000000000000001e-94 or 2.2e-32 < a

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 59.4%

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

   if -4.10000000000000001e-94 < a < 2.2e-32

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 79.5%

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

      3. fma-def 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in z around 0 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

      5. associate-*r/ 67.0%

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

   6. Simplified 67.0%

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

      1. clear-num 67.0%

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

      2. div-inv 67.0%

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

   8. Applied egg-rr 67.0%

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

   9. Taylor expanded in x around 0 47.7%

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

       1. associate-/l* 38.3%

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

       2. associate-*r/ 38.3%

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

       3. neg-mul-1 38.3%

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

       4. associate-/r/ 50.7%

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

       5. *-commutative 50.7%

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

       6. distribute-frac-neg 50.7%

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

   11. Simplified 50.7%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.3%

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

   1. associate-*l/ 97.7%

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

3. Simplified 97.7%

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

   1. *-commutative 97.7%

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

   2. clear-num 96.8%

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

   3. un-div-inv 97.7%

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

5. Applied egg-rr 97.7%

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

   1. div-inv 96.8%

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

   2. clear-num 97.7%

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

7. Applied egg-rr 97.7%

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

8. Final simplification 97.7%

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

Alternative 9: 38.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.3%

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

   1. +-commutative 90.3%

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

   2. associate-*r/ 92.1%

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

   3. fma-def 92.1%

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

3. Simplified 92.1%

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

4. Taylor expanded in y around 0 43.8%

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

5. Final simplification 43.8%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× 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 2023257 
(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)))