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

Percentage Accurate: 93.3% → 98.8%

Time: 11.4s

Alternatives: 10

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: 93.3% 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: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ y (/ a (- z t))))
     (if (<= t_1 2e+72) (+ x (/ t_1 a)) (+ x (* y (/ (- z t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (y / (a / (z - t)));
	} else if (t_1 <= 2e+72) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (y / (a / (z - t)));
	} else if (t_1 <= 2e+72) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (y / (a / (z - t)))
	elif t_1 <= 2e+72:
		tmp = x + (t_1 / a)
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t_1 <= 2e+72)
		tmp = Float64(x + Float64(t_1 / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (y / (a / (z - t)));
	elseif (t_1 <= 2e+72)
		tmp = x + (t_1 / a);
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+72], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0

   1. Initial program 71.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 1.99999999999999989e72

   1. Initial program 99.9%

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

   if 1.99999999999999989e72 < (*.f64 y (-.f64 z t))

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-*r/ 99.9%

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

      3. fma-udef 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. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y}}\\ t_2 := t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+226}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+282}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a y)))) (t_2 (* t (- (/ y a)))))
   (if (<= t -2.8e+161)
     t_2
     (if (<= t 4.5e+141)
       t_1
       (if (<= t 1.02e+226)
         (/ (* y t) (- a))
         (if (<= t 1.08e+282) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / y));
	double t_2 = t * -(y / a);
	double tmp;
	if (t <= -2.8e+161) {
		tmp = t_2;
	} else if (t <= 4.5e+141) {
		tmp = t_1;
	} else if (t <= 1.02e+226) {
		tmp = (y * t) / -a;
	} else if (t <= 1.08e+282) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / y))
    t_2 = t * -(y / a)
    if (t <= (-2.8d+161)) then
        tmp = t_2
    else if (t <= 4.5d+141) then
        tmp = t_1
    else if (t <= 1.02d+226) then
        tmp = (y * t) / -a
    else if (t <= 1.08d+282) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / y));
	double t_2 = t * -(y / a);
	double tmp;
	if (t <= -2.8e+161) {
		tmp = t_2;
	} else if (t <= 4.5e+141) {
		tmp = t_1;
	} else if (t <= 1.02e+226) {
		tmp = (y * t) / -a;
	} else if (t <= 1.08e+282) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / y))
	t_2 = t * -(y / a)
	tmp = 0
	if t <= -2.8e+161:
		tmp = t_2
	elif t <= 4.5e+141:
		tmp = t_1
	elif t <= 1.02e+226:
		tmp = (y * t) / -a
	elif t <= 1.08e+282:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / y)))
	t_2 = Float64(t * Float64(-Float64(y / a)))
	tmp = 0.0
	if (t <= -2.8e+161)
		tmp = t_2;
	elseif (t <= 4.5e+141)
		tmp = t_1;
	elseif (t <= 1.02e+226)
		tmp = Float64(Float64(y * t) / Float64(-a));
	elseif (t <= 1.08e+282)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / y));
	t_2 = t * -(y / a);
	tmp = 0.0;
	if (t <= -2.8e+161)
		tmp = t_2;
	elseif (t <= 4.5e+141)
		tmp = t_1;
	elseif (t <= 1.02e+226)
		tmp = (y * t) / -a;
	elseif (t <= 1.08e+282)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[t, -2.8e+161], t$95$2, If[LessEqual[t, 4.5e+141], t$95$1, If[LessEqual[t, 1.02e+226], N[(N[(y * t), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[t, 1.08e+282], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.80000000000000021e161 or 1.08000000000000004e282 < t

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. associate-*r/ 97.1%

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

      3. fma-udef 97.1%

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

   3. Simplified 97.1%

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

      1. fma-udef 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in z around 0 94.2%

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

      1. mul-1-neg 94.2%

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

      2. associate-*r/ 96.2%

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

      3. sub-neg 96.2%

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

   9. Simplified 96.2%

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

   10. Taylor expanded in x around 0 76.7%

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

       1. mul-1-neg 76.7%

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

       2. associate-*r/ 78.8%

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

       3. distribute-rgt-neg-out 78.8%

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

       4. distribute-neg-frac 78.8%

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

   12. Simplified 78.8%

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

   if -2.80000000000000021e161 < t < 4.5000000000000002e141 or 1.02e226 < t < 1.08000000000000004e282

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-*r/ 94.2%

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

      3. fma-udef 94.2%

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

   3. Simplified 94.2%

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

      1. fma-udef 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in z around inf 77.2%

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

      1. associate-*r/ 79.1%

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

   9. Simplified 79.1%

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

       1. associate-*r/ 77.2%

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

       2. *-commutative 77.2%

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

       3. associate-/l* 81.1%

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

   11. Applied egg-rr 81.1%

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

   if 4.5000000000000002e141 < t < 1.02e226

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      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. Step-by-step derivation

      1. fma-udef 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in z around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. associate-*r/ 87.0%

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

      3. sub-neg 87.0%

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

   9. Simplified 87.0%

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

   10. Taylor expanded in x around 0 66.7%

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

       1. mul-1-neg 66.7%

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

       2. associate-*r/ 65.0%

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

       3. distribute-rgt-neg-out 65.0%

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

       4. distribute-neg-frac 65.0%

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

   12. Simplified 65.0%

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

       1. frac-2neg 65.0%

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

       2. remove-double-neg 65.0%

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

       3. associate-*r/ 66.7%

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

   14. Applied egg-rr 66.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+226}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+282}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+229}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+229)))
     (+ x (/ y (/ a (- z t))))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+229)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+229)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+229):
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+229))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+229)))
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+229]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0 or 2e229 < (*.f64 y (-.f64 z t))

   1. Initial program 73.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 2e229

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty \lor \neg \left(y \cdot \left(z - t\right) \leq 2 \cdot 10^{+229}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+101} \lor \neg \left(t \leq 9.2 \cdot 10^{+68}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+101) (not (<= t 9.2e+68)))
   (- x (* t (/ y a)))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+101) || !(t <= 9.2e+68)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y / (a / z));
	}
	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 <= (-2.4d+101)) .or. (.not. (t <= 9.2d+68))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (y / (a / z))
    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 <= -2.4e+101) || !(t <= 9.2e+68)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+101) or not (t <= 9.2e+68):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+101) || !(t <= 9.2e+68))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+101) || ~((t <= 9.2e+68)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+101], N[Not[LessEqual[t, 9.2e+68]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999988e101 or 9.1999999999999999e68 < t

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-*r/ 89.7%

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

      3. fma-udef 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. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 89.7%

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

   6. Applied egg-rr 89.7%

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

   7. Taylor expanded in z around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. associate-*r/ 85.7%

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

      3. sub-neg 85.7%

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

   9. Simplified 85.7%

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

   if -2.39999999999999988e101 < t < 9.1999999999999999e68

   1. Initial program 92.9%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around 0 81.3%

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

      1. +-commutative 81.3%

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

      2. associate-/l* 86.3%

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

   7. Simplified 86.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+101} \lor \neg \left(t \leq 9.2 \cdot 10^{+68}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e+161)
   (* t (- (/ y a)))
   (if (<= t 2.9e+141) (+ x (/ (* y z) a)) (/ (* y t) (- a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+161) {
		tmp = t * -(y / a);
	} else if (t <= 2.9e+141) {
		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 <= (-1d+161)) then
        tmp = t * -(y / a)
    else if (t <= 2.9d+141) 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 <= -1e+161) {
		tmp = t * -(y / a);
	} else if (t <= 2.9e+141) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = (y * t) / -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e+161:
		tmp = t * -(y / a)
	elif t <= 2.9e+141:
		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 <= -1e+161)
		tmp = Float64(t * Float64(-Float64(y / a)));
	elseif (t <= 2.9e+141)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(Float64(y * t) / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1e+161)
		tmp = t * -(y / a);
	elseif (t <= 2.9e+141)
		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, -1e+161], N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 2.9e+141], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / (-a)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1e161

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-*r/ 96.5%

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

      3. fma-udef 96.5%

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

   3. Simplified 96.5%

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

      1. fma-udef 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in z around 0 92.9%

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

      1. mul-1-neg 92.9%

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

      2. associate-*r/ 95.4%

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

      3. sub-neg 95.4%

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

   9. Simplified 95.4%

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

   10. Taylor expanded in x around 0 71.5%

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

       1. mul-1-neg 71.5%

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

       2. associate-*r/ 74.0%

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

       3. distribute-rgt-neg-out 74.0%

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

       4. distribute-neg-frac 74.0%

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

   12. Simplified 74.0%

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

   if -1e161 < t < 2.90000000000000007e141

   1. Initial program 91.9%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 78.2%

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

   if 2.90000000000000007e141 < t

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. associate-*r/ 97.6%

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

      3. fma-udef 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in z around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. associate-*r/ 86.8%

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

      3. sub-neg 86.8%

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

   9. Simplified 86.8%

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

   10. Taylor expanded in x around 0 61.0%

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

       1. mul-1-neg 61.0%

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

       2. associate-*r/ 60.9%

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

       3. distribute-rgt-neg-out 60.9%

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

       4. distribute-neg-frac 60.9%

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

   12. Simplified 60.9%

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

       1. frac-2neg 60.9%

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

       2. remove-double-neg 60.9%

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

       3. associate-*r/ 61.0%

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

   14. Applied egg-rr 61.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+141}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+103)
   (* t (- (/ y a)))
   (if (<= t 2.7e+141) (+ x (* y (/ z a))) (/ (* y t) (- a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+103) {
		tmp = t * -(y / a);
	} else if (t <= 2.7e+141) {
		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 <= (-1.7d+103)) then
        tmp = t * -(y / a)
    else if (t <= 2.7d+141) 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 <= -1.7e+103) {
		tmp = t * -(y / a);
	} else if (t <= 2.7e+141) {
		tmp = x + (y * (z / a));
	} else {
		tmp = (y * t) / -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+103:
		tmp = t * -(y / a)
	elif t <= 2.7e+141:
		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 <= -1.7e+103)
		tmp = Float64(t * Float64(-Float64(y / a)));
	elseif (t <= 2.7e+141)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(Float64(y * t) / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+103)
		tmp = t * -(y / a);
	elseif (t <= 2.7e+141)
		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, -1.7e+103], N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 2.7e+141], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / (-a)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6999999999999999e103

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. associate-*r/ 91.0%

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

      3. fma-udef 91.0%

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

   3. Simplified 91.0%

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

      1. fma-udef 91.0%

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

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in z around 0 91.3%

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

      1. mul-1-neg 91.3%

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

      2. associate-*r/ 93.4%

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

      3. sub-neg 93.4%

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

   9. Simplified 93.4%

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

   10. Taylor expanded in x around 0 67.8%

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

       1. mul-1-neg 67.8%

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

       2. associate-*r/ 69.8%

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

       3. distribute-rgt-neg-out 69.8%

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

       4. distribute-neg-frac 69.8%

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

   12. Simplified 69.8%

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

   if -1.6999999999999999e103 < t < 2.7000000000000001e141

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-*r/ 94.7%

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

      3. fma-udef 94.7%

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

   3. Simplified 94.7%

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

      1. fma-udef 94.7%

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

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in z around inf 79.1%

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

      1. associate-*r/ 81.7%

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

   9. Simplified 81.7%

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

   if 2.7000000000000001e141 < t

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. associate-*r/ 97.6%

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

      3. fma-udef 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in z around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. associate-*r/ 86.8%

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

      3. sub-neg 86.8%

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

   9. Simplified 86.8%

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

   10. Taylor expanded in x around 0 61.0%

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

       1. mul-1-neg 61.0%

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

       2. associate-*r/ 60.9%

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

       3. distribute-rgt-neg-out 60.9%

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

       4. distribute-neg-frac 60.9%

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

   12. Simplified 60.9%

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

       1. frac-2neg 60.9%

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

       2. remove-double-neg 60.9%

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

       3. associate-*r/ 61.0%

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

   14. Applied egg-rr 61.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+141}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e+103)
   (* t (- (/ y a)))
   (if (<= t 2.85e+141) (+ x (/ y (/ a z))) (/ (* y t) (- a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+103) {
		tmp = t * -(y / a);
	} else if (t <= 2.85e+141) {
		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 <= (-5.6d+103)) then
        tmp = t * -(y / a)
    else if (t <= 2.85d+141) 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 <= -5.6e+103) {
		tmp = t * -(y / a);
	} else if (t <= 2.85e+141) {
		tmp = x + (y / (a / z));
	} else {
		tmp = (y * t) / -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e+103:
		tmp = t * -(y / a)
	elif t <= 2.85e+141:
		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 <= -5.6e+103)
		tmp = Float64(t * Float64(-Float64(y / a)));
	elseif (t <= 2.85e+141)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(Float64(y * t) / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e+103)
		tmp = t * -(y / a);
	elseif (t <= 2.85e+141)
		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, -5.6e+103], N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 2.85e+141], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / (-a)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.60000000000000017e103

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. associate-*r/ 91.0%

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

      3. fma-udef 91.0%

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

   3. Simplified 91.0%

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

      1. fma-udef 91.0%

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

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in z around 0 91.3%

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

      1. mul-1-neg 91.3%

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

      2. associate-*r/ 93.4%

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

      3. sub-neg 93.4%

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

   9. Simplified 93.4%

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

   10. Taylor expanded in x around 0 67.8%

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

       1. mul-1-neg 67.8%

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

       2. associate-*r/ 69.8%

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

       3. distribute-rgt-neg-out 69.8%

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

       4. distribute-neg-frac 69.8%

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

   12. Simplified 69.8%

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

   if -5.60000000000000017e103 < t < 2.84999999999999999e141

   1. Initial program 91.7%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 82.6%

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

   7. Simplified 82.6%

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

   if 2.84999999999999999e141 < t

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. associate-*r/ 97.6%

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

      3. fma-udef 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in z around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. associate-*r/ 86.8%

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

      3. sub-neg 86.8%

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

   9. Simplified 86.8%

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

   10. Taylor expanded in x around 0 61.0%

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

       1. mul-1-neg 61.0%

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

       2. associate-*r/ 60.9%

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

       3. distribute-rgt-neg-out 60.9%

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

       4. distribute-neg-frac 60.9%

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

   12. Simplified 60.9%

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

       1. frac-2neg 60.9%

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

       2. remove-double-neg 60.9%

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

       3. associate-*r/ 61.0%

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

   14. Applied egg-rr 61.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.5e+60) x (if (<= x 2.25e+63) (* t (- (/ y a))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.5e+60) {
		tmp = x;
	} else if (x <= 2.25e+63) {
		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 (x <= (-6.5d+60)) then
        tmp = x
    else if (x <= 2.25d+63) 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 (x <= -6.5e+60) {
		tmp = x;
	} else if (x <= 2.25e+63) {
		tmp = t * -(y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.5e+60:
		tmp = x
	elif x <= 2.25e+63:
		tmp = t * -(y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.5e+60)
		tmp = x;
	elseif (x <= 2.25e+63)
		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 (x <= -6.5e+60)
		tmp = x;
	elseif (x <= 2.25e+63)
		tmp = t * -(y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.5e+60], x, If[LessEqual[x, 2.25e+63], N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999931e60 or 2.25000000000000008e63 < x

   1. Initial program 94.7%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 69.3%

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

   if -6.49999999999999931e60 < x < 2.25000000000000008e63

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-*r/ 94.1%

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

      3. fma-udef 94.2%

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

   3. Simplified 94.2%

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

      1. fma-udef 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in z around 0 62.8%

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

      1. mul-1-neg 62.8%

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

      2. associate-*r/ 63.5%

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

      3. sub-neg 63.5%

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

   9. Simplified 63.5%

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

   10. Taylor expanded in x around 0 44.6%

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

       1. mul-1-neg 44.6%

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

       2. associate-*r/ 45.6%

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

       3. distribute-rgt-neg-out 45.6%

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

       4. distribute-neg-frac 45.6%

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

   12. Simplified 45.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.8% 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 93.0%

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

   1. associate-/l* 95.4%

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

3. Simplified 95.4%

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

5. Final simplification 95.4%

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

Alternative 10: 39.3% 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 93.0%

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

   1. associate-/l* 95.4%

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

3. Simplified 95.4%

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

5. Taylor expanded in x around inf 41.0%

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

6. Final simplification 41.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% 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 2024021 
(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)))