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

Percentage Accurate: 93.1% → 99.5%

Time: 11.9s

Alternatives: 14

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: 93.1% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+208}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+208)))
     (+ 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 = (z - t) * y;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+208)) {
		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 = (z - t) * y;
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+208)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+208):
		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(Float64(z - t) * y)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+208))
		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 = (z - t) * y;
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+208)))
		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[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+208]], $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 2e208 < (*.f64 y (-.f64 z t))

   1. Initial program 71.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 2e208

   1. Initial program 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -\infty \lor \neg \left(\left(z - t\right) \cdot y \leq 2 \cdot 10^{+208}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-t}{a}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-172}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t) a))))
   (if (<= t -8.6e+136)
     t_1
     (if (<= t 1.8e-245)
       x
       (if (<= t 1.7e-172)
         (/ y (/ a z))
         (if (<= t 5.2e-128) x (if (<= t 2.55e-12) (* z (/ y a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-t / a);
	double tmp;
	if (t <= -8.6e+136) {
		tmp = t_1;
	} else if (t <= 1.8e-245) {
		tmp = x;
	} else if (t <= 1.7e-172) {
		tmp = y / (a / z);
	} else if (t <= 5.2e-128) {
		tmp = x;
	} else if (t <= 2.55e-12) {
		tmp = z * (y / a);
	} else {
		tmp = 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 = y * (-t / a)
    if (t <= (-8.6d+136)) then
        tmp = t_1
    else if (t <= 1.8d-245) then
        tmp = x
    else if (t <= 1.7d-172) then
        tmp = y / (a / z)
    else if (t <= 5.2d-128) then
        tmp = x
    else if (t <= 2.55d-12) then
        tmp = z * (y / a)
    else
        tmp = 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 = y * (-t / a);
	double tmp;
	if (t <= -8.6e+136) {
		tmp = t_1;
	} else if (t <= 1.8e-245) {
		tmp = x;
	} else if (t <= 1.7e-172) {
		tmp = y / (a / z);
	} else if (t <= 5.2e-128) {
		tmp = x;
	} else if (t <= 2.55e-12) {
		tmp = z * (y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-t / a)
	tmp = 0
	if t <= -8.6e+136:
		tmp = t_1
	elif t <= 1.8e-245:
		tmp = x
	elif t <= 1.7e-172:
		tmp = y / (a / z)
	elif t <= 5.2e-128:
		tmp = x
	elif t <= 2.55e-12:
		tmp = z * (y / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-t) / a))
	tmp = 0.0
	if (t <= -8.6e+136)
		tmp = t_1;
	elseif (t <= 1.8e-245)
		tmp = x;
	elseif (t <= 1.7e-172)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 5.2e-128)
		tmp = x;
	elseif (t <= 2.55e-12)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-t / a);
	tmp = 0.0;
	if (t <= -8.6e+136)
		tmp = t_1;
	elseif (t <= 1.8e-245)
		tmp = x;
	elseif (t <= 1.7e-172)
		tmp = y / (a / z);
	elseif (t <= 5.2e-128)
		tmp = x;
	elseif (t <= 2.55e-12)
		tmp = z * (y / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+136], t$95$1, If[LessEqual[t, 1.8e-245], x, If[LessEqual[t, 1.7e-172], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-128], x, If[LessEqual[t, 2.55e-12], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.5999999999999997e136 or 2.54999999999999984e-12 < t

   1. Initial program 86.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. associate-*r/ 88.8%

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

      2. neg-mul-1 88.8%

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

      3. unsub-neg 88.8%

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

      4. associate-*r/ 81.7%

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

      5. associate-/l* 87.9%

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

      6. associate-/r/ 86.6%

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

   7. Simplified 86.6%

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

      1. associate-*l/ 81.7%

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

      2. associate-/l* 87.9%

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

   9. Applied egg-rr 87.9%

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

   10. Taylor expanded in x around 0 56.9%

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

       1. mul-1-neg 56.9%

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

       2. associate-*l/ 61.8%

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

       3. *-commutative 61.8%

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

       4. distribute-lft-neg-in 61.8%

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

   12. Simplified 61.8%

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

   if -8.5999999999999997e136 < t < 1.8e-245 or 1.6999999999999999e-172 < t < 5.19999999999999961e-128

   1. Initial program 97.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in x around inf 52.3%

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

   if 1.8e-245 < t < 1.6999999999999999e-172

   1. Initial program 85.4%

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

   5. Taylor expanded in t around 0 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-*l/ 92.6%

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

      3. *-commutative 92.6%

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

      4. fma-def 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in z around inf 55.7%

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

      1. associate-*l/ 62.8%

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

   10. Simplified 62.8%

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

       1. associate-*l/ 55.7%

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

       2. associate-/l* 70.1%

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

   12. Applied egg-rr 70.1%

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

   if 5.19999999999999961e-128 < t < 2.54999999999999984e-12

   1. Initial program 89.7%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. associate-*l/ 83.0%

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

      3. *-commutative 83.0%

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

      4. fma-def 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in z around inf 50.5%

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

      1. associate-*l/ 62.0%

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

   10. Simplified 62.0%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-172}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-176}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+139)
   (* y (/ (- t) a))
   (if (<= t 1.9e-245)
     x
     (if (<= t 8e-176)
       (/ y (/ a z))
       (if (<= t 5.8e-124)
         x
         (if (<= t 1.8e-12) (* z (/ y a)) (* t (/ y (- a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+139) {
		tmp = y * (-t / a);
	} else if (t <= 1.9e-245) {
		tmp = x;
	} else if (t <= 8e-176) {
		tmp = y / (a / z);
	} else if (t <= 5.8e-124) {
		tmp = x;
	} else if (t <= 1.8e-12) {
		tmp = z * (y / a);
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.7d+139)) then
        tmp = y * (-t / a)
    else if (t <= 1.9d-245) then
        tmp = x
    else if (t <= 8d-176) then
        tmp = y / (a / z)
    else if (t <= 5.8d-124) then
        tmp = x
    else if (t <= 1.8d-12) then
        tmp = z * (y / a)
    else
        tmp = t * (y / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+139) {
		tmp = y * (-t / a);
	} else if (t <= 1.9e-245) {
		tmp = x;
	} else if (t <= 8e-176) {
		tmp = y / (a / z);
	} else if (t <= 5.8e-124) {
		tmp = x;
	} else if (t <= 1.8e-12) {
		tmp = z * (y / a);
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+139:
		tmp = y * (-t / a)
	elif t <= 1.9e-245:
		tmp = x
	elif t <= 8e-176:
		tmp = y / (a / z)
	elif t <= 5.8e-124:
		tmp = x
	elif t <= 1.8e-12:
		tmp = z * (y / a)
	else:
		tmp = t * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+139)
		tmp = Float64(y * Float64(Float64(-t) / a));
	elseif (t <= 1.9e-245)
		tmp = x;
	elseif (t <= 8e-176)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 5.8e-124)
		tmp = x;
	elseif (t <= 1.8e-12)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = Float64(t * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+139)
		tmp = y * (-t / a);
	elseif (t <= 1.9e-245)
		tmp = x;
	elseif (t <= 8e-176)
		tmp = y / (a / z);
	elseif (t <= 5.8e-124)
		tmp = x;
	elseif (t <= 1.8e-12)
		tmp = z * (y / a);
	else
		tmp = t * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+139], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-245], x, If[LessEqual[t, 8e-176], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-124], x, If[LessEqual[t, 1.8e-12], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.6999999999999998e139

   1. Initial program 84.3%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around 0 84.3%

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

      1. associate-*r/ 96.3%

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

      2. neg-mul-1 96.3%

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

      3. unsub-neg 96.3%

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

      4. associate-*r/ 84.3%

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

      5. associate-/l* 96.2%

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

      6. associate-/r/ 95.6%

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

   7. Simplified 95.6%

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

      1. associate-*l/ 84.3%

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

      2. associate-/l* 96.2%

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

   9. Applied egg-rr 96.2%

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

   10. Taylor expanded in x around 0 63.2%

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

       1. mul-1-neg 63.2%

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

       2. associate-*l/ 74.9%

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

       3. *-commutative 74.9%

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

       4. distribute-lft-neg-in 74.9%

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

   12. Simplified 74.9%

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

   if -2.6999999999999998e139 < t < 1.9e-245 or 8e-176 < t < 5.8000000000000004e-124

   1. Initial program 97.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in x around inf 52.3%

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

   if 1.9e-245 < t < 8e-176

   1. Initial program 85.4%

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

   5. Taylor expanded in t around 0 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-*l/ 92.6%

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

      3. *-commutative 92.6%

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

      4. fma-def 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in z around inf 55.7%

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

      1. associate-*l/ 62.8%

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

   10. Simplified 62.8%

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

       1. associate-*l/ 55.7%

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

       2. associate-/l* 70.1%

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

   12. Applied egg-rr 70.1%

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

   if 5.8000000000000004e-124 < t < 1.8e-12

   1. Initial program 89.7%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. associate-*l/ 83.0%

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

      3. *-commutative 83.0%

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

      4. fma-def 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in z around inf 50.5%

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

      1. associate-*l/ 62.0%

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

   10. Simplified 62.0%

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

   if 1.8e-12 < t

   1. Initial program 87.8%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in z around 0 80.8%

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

      1. associate-*r/ 86.3%

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

      2. neg-mul-1 86.3%

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

      3. unsub-neg 86.3%

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

      4. associate-*r/ 80.8%

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

      5. associate-/l* 85.1%

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

      6. associate-/r/ 83.6%

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

   7. Simplified 83.6%

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

      1. associate-*l/ 80.8%

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

      2. associate-/l* 85.1%

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

   9. Applied egg-rr 85.1%

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

   10. Taylor expanded in x around 0 54.8%

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

       1. mul-1-neg 54.8%

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

       2. associate-*l/ 57.4%

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

       3. *-commutative 57.4%

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

       4. distribute-lft-neg-in 57.4%

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

   12. Simplified 57.4%

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

       1. associate-*r/ 54.8%

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

       2. frac-2neg 54.8%

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

       3. add-sqr-sqrt 24.0%

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

       4. sqrt-unprod 26.3%

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

       5. sqr-neg 26.3%

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

       6. sqrt-unprod 2.2%

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

       7. add-sqr-sqrt 3.3%

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

       8. distribute-lft-neg-out 3.3%

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

       9. add-sqr-sqrt 1.2%

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

       10. sqrt-unprod 25.2%

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

       11. sqr-neg 25.2%

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

       12. sqrt-unprod 30.6%

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

       13. add-sqr-sqrt 54.8%

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

   14. Applied egg-rr 54.8%

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

       1. associate-/l* 57.4%

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

       2. associate-/r/ 59.9%

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

   16. Simplified 59.9%

       \[\leadsto \color{blue}{\frac{y}{-a} \cdot t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-176}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+136)
   (/ y (/ (- a) t))
   (if (<= t 6.8e-248)
     x
     (if (<= t 2.5e-175)
       (/ y (/ a z))
       (if (<= t 1.45e-124)
         x
         (if (<= t 3.15e-12) (* z (/ y a)) (* t (/ y (- a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+136) {
		tmp = y / (-a / t);
	} else if (t <= 6.8e-248) {
		tmp = x;
	} else if (t <= 2.5e-175) {
		tmp = y / (a / z);
	} else if (t <= 1.45e-124) {
		tmp = x;
	} else if (t <= 3.15e-12) {
		tmp = z * (y / a);
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.5d+136)) then
        tmp = y / (-a / t)
    else if (t <= 6.8d-248) then
        tmp = x
    else if (t <= 2.5d-175) then
        tmp = y / (a / z)
    else if (t <= 1.45d-124) then
        tmp = x
    else if (t <= 3.15d-12) then
        tmp = z * (y / a)
    else
        tmp = t * (y / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+136) {
		tmp = y / (-a / t);
	} else if (t <= 6.8e-248) {
		tmp = x;
	} else if (t <= 2.5e-175) {
		tmp = y / (a / z);
	} else if (t <= 1.45e-124) {
		tmp = x;
	} else if (t <= 3.15e-12) {
		tmp = z * (y / a);
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+136:
		tmp = y / (-a / t)
	elif t <= 6.8e-248:
		tmp = x
	elif t <= 2.5e-175:
		tmp = y / (a / z)
	elif t <= 1.45e-124:
		tmp = x
	elif t <= 3.15e-12:
		tmp = z * (y / a)
	else:
		tmp = t * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+136)
		tmp = Float64(y / Float64(Float64(-a) / t));
	elseif (t <= 6.8e-248)
		tmp = x;
	elseif (t <= 2.5e-175)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.45e-124)
		tmp = x;
	elseif (t <= 3.15e-12)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = Float64(t * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e+136)
		tmp = y / (-a / t);
	elseif (t <= 6.8e-248)
		tmp = x;
	elseif (t <= 2.5e-175)
		tmp = y / (a / z);
	elseif (t <= 1.45e-124)
		tmp = x;
	elseif (t <= 3.15e-12)
		tmp = z * (y / a);
	else
		tmp = t * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+136], N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-248], x, If[LessEqual[t, 2.5e-175], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-124], x, If[LessEqual[t, 3.15e-12], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.4999999999999998e136

   1. Initial program 84.3%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around 0 84.3%

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

      1. associate-*r/ 96.3%

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

      2. neg-mul-1 96.3%

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

      3. unsub-neg 96.3%

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

      4. associate-*r/ 84.3%

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

      5. associate-/l* 96.2%

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

      6. associate-/r/ 95.6%

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

   7. Simplified 95.6%

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

      1. associate-*l/ 84.3%

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

      2. associate-/l* 96.2%

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

   9. Applied egg-rr 96.2%

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

   10. Taylor expanded in x around 0 63.2%

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

       1. mul-1-neg 63.2%

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

       2. associate-*l/ 74.9%

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

       3. *-commutative 74.9%

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

       4. distribute-lft-neg-in 74.9%

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

   12. Simplified 74.9%

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

       1. associate-*r/ 63.2%

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

       2. frac-2neg 63.2%

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

       3. add-sqr-sqrt 21.5%

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

       4. sqrt-unprod 22.5%

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

       5. sqr-neg 22.5%

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

       6. sqrt-unprod 0.8%

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

       7. add-sqr-sqrt 1.3%

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

       8. distribute-lft-neg-out 1.3%

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

       9. add-sqr-sqrt 0.4%

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

       10. sqrt-unprod 40.5%

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

       11. sqr-neg 40.5%

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

       12. sqrt-unprod 41.5%

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

       13. add-sqr-sqrt 63.2%

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

   14. Applied egg-rr 63.2%

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

       1. associate-/l* 74.9%

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

   16. Simplified 74.9%

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

   if -6.4999999999999998e136 < t < 6.7999999999999996e-248 or 2.5e-175 < t < 1.4500000000000001e-124

   1. Initial program 97.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in x around inf 52.3%

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

   if 6.7999999999999996e-248 < t < 2.5e-175

   1. Initial program 85.4%

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

   5. Taylor expanded in t around 0 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-*l/ 92.6%

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

      3. *-commutative 92.6%

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

      4. fma-def 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in z around inf 55.7%

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

      1. associate-*l/ 62.8%

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

   10. Simplified 62.8%

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

       1. associate-*l/ 55.7%

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

       2. associate-/l* 70.1%

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

   12. Applied egg-rr 70.1%

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

   if 1.4500000000000001e-124 < t < 3.1500000000000001e-12

   1. Initial program 89.7%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. associate-*l/ 83.0%

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

      3. *-commutative 83.0%

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

      4. fma-def 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in z around inf 50.5%

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

      1. associate-*l/ 62.0%

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

   10. Simplified 62.0%

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

   if 3.1500000000000001e-12 < t

   1. Initial program 87.8%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in z around 0 80.8%

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

      1. associate-*r/ 86.3%

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

      2. neg-mul-1 86.3%

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

      3. unsub-neg 86.3%

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

      4. associate-*r/ 80.8%

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

      5. associate-/l* 85.1%

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

      6. associate-/r/ 83.6%

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

   7. Simplified 83.6%

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

      1. associate-*l/ 80.8%

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

      2. associate-/l* 85.1%

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

   9. Applied egg-rr 85.1%

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

   10. Taylor expanded in x around 0 54.8%

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

       1. mul-1-neg 54.8%

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

       2. associate-*l/ 57.4%

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

       3. *-commutative 57.4%

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

       4. distribute-lft-neg-in 57.4%

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

   12. Simplified 57.4%

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

       1. associate-*r/ 54.8%

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

       2. frac-2neg 54.8%

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

       3. add-sqr-sqrt 24.0%

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

       4. sqrt-unprod 26.3%

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

       5. sqr-neg 26.3%

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

       6. sqrt-unprod 2.2%

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

       7. add-sqr-sqrt 3.3%

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

       8. distribute-lft-neg-out 3.3%

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

       9. add-sqr-sqrt 1.2%

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

       10. sqrt-unprod 25.2%

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

       11. sqr-neg 25.2%

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

       12. sqrt-unprod 30.6%

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

       13. add-sqr-sqrt 54.8%

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

   14. Applied egg-rr 54.8%

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

       1. associate-/l* 57.4%

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

       2. associate-/r/ 59.9%

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

   16. Simplified 59.9%

       \[\leadsto \color{blue}{\frac{y}{-a} \cdot t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+151}:\\ \;\;\;\;\frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 44000000000 \lor \neg \left(t \leq 7.2 \cdot 10^{+75}\right) \land t \leq 1.45 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.8e+151)
   (/ y (/ (- a) t))
   (if (or (<= t 44000000000.0) (and (not (<= t 7.2e+75)) (<= t 1.45e+112)))
     (+ x (/ (* z y) a))
     (* t (/ y (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e+151) {
		tmp = y / (-a / t);
	} else if ((t <= 44000000000.0) || (!(t <= 7.2e+75) && (t <= 1.45e+112))) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.8d+151)) then
        tmp = y / (-a / t)
    else if ((t <= 44000000000.0d0) .or. (.not. (t <= 7.2d+75)) .and. (t <= 1.45d+112)) then
        tmp = x + ((z * y) / a)
    else
        tmp = t * (y / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e+151) {
		tmp = y / (-a / t);
	} else if ((t <= 44000000000.0) || (!(t <= 7.2e+75) && (t <= 1.45e+112))) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.8e+151:
		tmp = y / (-a / t)
	elif (t <= 44000000000.0) or (not (t <= 7.2e+75) and (t <= 1.45e+112)):
		tmp = x + ((z * y) / a)
	else:
		tmp = t * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.8e+151)
		tmp = Float64(y / Float64(Float64(-a) / t));
	elseif ((t <= 44000000000.0) || (!(t <= 7.2e+75) && (t <= 1.45e+112)))
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = Float64(t * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.8e+151)
		tmp = y / (-a / t);
	elseif ((t <= 44000000000.0) || (~((t <= 7.2e+75)) && (t <= 1.45e+112)))
		tmp = x + ((z * y) / a);
	else
		tmp = t * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.8e+151], N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 44000000000.0], And[N[Not[LessEqual[t, 7.2e+75]], $MachinePrecision], LessEqual[t, 1.45e+112]]], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.7999999999999998e151

   1. Initial program 83.6%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around 0 83.6%

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

      1. associate-*r/ 96.1%

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

      2. neg-mul-1 96.1%

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

      3. unsub-neg 96.1%

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

      4. associate-*r/ 83.6%

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

      5. associate-/l* 96.0%

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

      6. associate-/r/ 95.4%

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

   7. Simplified 95.4%

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

      1. associate-*l/ 83.6%

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

      2. associate-/l* 96.0%

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

   9. Applied egg-rr 96.0%

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

   10. Taylor expanded in x around 0 61.6%

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

       1. mul-1-neg 61.6%

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

       2. associate-*l/ 73.8%

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

       3. *-commutative 73.8%

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

       4. distribute-lft-neg-in 73.8%

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

   12. Simplified 73.8%

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

       1. associate-*r/ 61.6%

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

       2. frac-2neg 61.6%

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

       3. add-sqr-sqrt 22.4%

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

       4. sqrt-unprod 23.5%

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

       5. sqr-neg 23.5%

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

       6. sqrt-unprod 0.9%

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

       7. add-sqr-sqrt 1.3%

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

       8. distribute-lft-neg-out 1.3%

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

       9. add-sqr-sqrt 0.4%

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

       10. sqrt-unprod 37.9%

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

       11. sqr-neg 37.9%

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

       12. sqrt-unprod 39.0%

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

       13. add-sqr-sqrt 61.6%

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

   14. Applied egg-rr 61.6%

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

       1. associate-/l* 73.8%

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

   16. Simplified 73.8%

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

   if -9.7999999999999998e151 < t < 4.4e10 or 7.2e75 < t < 1.4500000000000001e112

   1. Initial program 95.2%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around inf 85.2%

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

   if 4.4e10 < t < 7.2e75 or 1.4500000000000001e112 < t

   1. Initial program 85.3%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around 0 86.9%

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

      1. associate-*r/ 93.5%

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

      2. neg-mul-1 93.5%

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

      3. unsub-neg 93.5%

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

      4. associate-*r/ 86.9%

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

      5. associate-/l* 92.0%

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

      6. associate-/r/ 90.2%

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

   7. Simplified 90.2%

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

      1. associate-*l/ 86.9%

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

      2. associate-/l* 92.0%

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

   9. Applied egg-rr 92.0%

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

   10. Taylor expanded in x around 0 60.3%

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

       1. mul-1-neg 60.3%

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

       2. associate-*l/ 63.5%

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

       3. *-commutative 63.5%

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

       4. distribute-lft-neg-in 63.5%

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

   12. Simplified 63.5%

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

       1. associate-*r/ 60.3%

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

       2. frac-2neg 60.3%

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

       3. add-sqr-sqrt 27.1%

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

       4. sqrt-unprod 27.8%

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

       5. sqr-neg 27.8%

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

       6. sqrt-unprod 0.6%

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

       7. add-sqr-sqrt 1.6%

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

       8. distribute-lft-neg-out 1.6%

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

       9. add-sqr-sqrt 1.1%

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

       10. sqrt-unprod 26.3%

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

       11. sqr-neg 26.3%

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

       12. sqrt-unprod 33.0%

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

       13. add-sqr-sqrt 60.3%

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

   14. Applied egg-rr 60.3%

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

       1. associate-/l* 63.5%

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

       2. associate-/r/ 66.5%

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

   16. Simplified 66.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+151}:\\ \;\;\;\;\frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 44000000000 \lor \neg \left(t \leq 7.2 \cdot 10^{+75}\right) \land t \leq 1.45 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := \frac{y}{\frac{-a}{t}}\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 46000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (/ y (/ (- a) t))))
   (if (<= t -2.55e+151)
     t_2
     (if (<= t 46000000000.0)
       t_1
       (if (<= t 1.7e+47) t_2 (if (<= t 1.56e+112) t_1 (* t (/ y (- a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = y / (-a / t);
	double tmp;
	if (t <= -2.55e+151) {
		tmp = t_2;
	} else if (t <= 46000000000.0) {
		tmp = t_1;
	} else if (t <= 1.7e+47) {
		tmp = t_2;
	} else if (t <= 1.56e+112) {
		tmp = t_1;
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = y / (-a / t)
    if (t <= (-2.55d+151)) then
        tmp = t_2
    else if (t <= 46000000000.0d0) then
        tmp = t_1
    else if (t <= 1.7d+47) then
        tmp = t_2
    else if (t <= 1.56d+112) then
        tmp = t_1
    else
        tmp = t * (y / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = y / (-a / t);
	double tmp;
	if (t <= -2.55e+151) {
		tmp = t_2;
	} else if (t <= 46000000000.0) {
		tmp = t_1;
	} else if (t <= 1.7e+47) {
		tmp = t_2;
	} else if (t <= 1.56e+112) {
		tmp = t_1;
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = y / (-a / t)
	tmp = 0
	if t <= -2.55e+151:
		tmp = t_2
	elif t <= 46000000000.0:
		tmp = t_1
	elif t <= 1.7e+47:
		tmp = t_2
	elif t <= 1.56e+112:
		tmp = t_1
	else:
		tmp = t * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(y / Float64(Float64(-a) / t))
	tmp = 0.0
	if (t <= -2.55e+151)
		tmp = t_2;
	elseif (t <= 46000000000.0)
		tmp = t_1;
	elseif (t <= 1.7e+47)
		tmp = t_2;
	elseif (t <= 1.56e+112)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = y / (-a / t);
	tmp = 0.0;
	if (t <= -2.55e+151)
		tmp = t_2;
	elseif (t <= 46000000000.0)
		tmp = t_1;
	elseif (t <= 1.7e+47)
		tmp = t_2;
	elseif (t <= 1.56e+112)
		tmp = t_1;
	else
		tmp = t * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.55e+151], t$95$2, If[LessEqual[t, 46000000000.0], t$95$1, If[LessEqual[t, 1.7e+47], t$95$2, If[LessEqual[t, 1.56e+112], t$95$1, N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.54999999999999998e151 or 4.6e10 < t < 1.6999999999999999e47

   1. Initial program 79.9%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around 0 79.9%

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

      1. associate-*r/ 97.2%

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

      2. neg-mul-1 97.2%

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

      3. unsub-neg 97.2%

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

      4. associate-*r/ 79.9%

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

      5. associate-/l* 97.2%

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

      6. associate-/r/ 96.7%

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

   7. Simplified 96.7%

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

      1. associate-*l/ 79.9%

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

      2. associate-/l* 97.2%

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

   9. Applied egg-rr 97.2%

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

   10. Taylor expanded in x around 0 58.9%

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

       1. mul-1-neg 58.9%

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

       2. associate-*l/ 73.1%

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

       3. *-commutative 73.1%

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

       4. distribute-lft-neg-in 73.1%

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

   12. Simplified 73.1%

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

       1. associate-*r/ 58.9%

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

       2. frac-2neg 58.9%

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

       3. add-sqr-sqrt 22.5%

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

       4. sqrt-unprod 23.1%

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

       5. sqr-neg 23.1%

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

       6. sqrt-unprod 0.7%

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

       7. add-sqr-sqrt 1.2%

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

       8. distribute-lft-neg-out 1.2%

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

       9. add-sqr-sqrt 0.5%

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

       10. sqrt-unprod 32.9%

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

       11. sqr-neg 32.9%

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

       12. sqrt-unprod 36.3%

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

       13. add-sqr-sqrt 58.9%

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

   14. Applied egg-rr 58.9%

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

       1. associate-/l* 73.2%

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

   16. Simplified 73.2%

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

   if -2.54999999999999998e151 < t < 4.6e10 or 1.6999999999999999e47 < t < 1.55999999999999992e112

   1. Initial program 94.8%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-*l/ 87.5%

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

      3. *-commutative 87.5%

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

   7. Simplified 87.5%

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

   if 1.55999999999999992e112 < t

   1. Initial program 88.7%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around 0 90.9%

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

      1. associate-*r/ 93.4%

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

      2. neg-mul-1 93.4%

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

      3. unsub-neg 93.4%

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

      4. associate-*r/ 90.9%

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

      5. associate-/l* 91.3%

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

      6. associate-/r/ 88.9%

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

   7. Simplified 88.9%

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

      1. associate-*l/ 90.9%

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

      2. associate-/l* 91.3%

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

   9. Applied egg-rr 91.3%

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

   10. Taylor expanded in x around 0 63.4%

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

       1. mul-1-neg 63.4%

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

       2. associate-*l/ 63.4%

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

       3. *-commutative 63.4%

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

       4. distribute-lft-neg-in 63.4%

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

   12. Simplified 63.4%

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

       1. associate-*r/ 63.4%

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

       2. frac-2neg 63.4%

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

       3. add-sqr-sqrt 27.2%

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

       4. sqrt-unprod 28.1%

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

       5. sqr-neg 28.1%

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

       6. sqrt-unprod 0.7%

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

       7. add-sqr-sqrt 1.7%

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

       8. distribute-lft-neg-out 1.7%

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

       9. add-sqr-sqrt 1.0%

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

       10. sqrt-unprod 28.5%

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

       11. sqr-neg 28.5%

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

       12. sqrt-unprod 36.0%

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

       13. add-sqr-sqrt 63.4%

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

   14. Applied egg-rr 63.4%

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

       1. associate-/l* 63.4%

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

       2. associate-/r/ 67.5%

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

   16. Simplified 67.5%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+151}:\\ \;\;\;\;\frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 46000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.56 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+112)
   x
   (if (<= a -5e+45)
     (* y (/ z a))
     (if (<= a -1.56e-21) x (if (<= a 1.4e-67) (* z (/ y a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+112) {
		tmp = x;
	} else if (a <= -5e+45) {
		tmp = y * (z / a);
	} else if (a <= -1.56e-21) {
		tmp = x;
	} else if (a <= 1.4e-67) {
		tmp = z * (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 <= (-9.5d+112)) then
        tmp = x
    else if (a <= (-5d+45)) then
        tmp = y * (z / a)
    else if (a <= (-1.56d-21)) then
        tmp = x
    else if (a <= 1.4d-67) then
        tmp = z * (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 <= -9.5e+112) {
		tmp = x;
	} else if (a <= -5e+45) {
		tmp = y * (z / a);
	} else if (a <= -1.56e-21) {
		tmp = x;
	} else if (a <= 1.4e-67) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+112:
		tmp = x
	elif a <= -5e+45:
		tmp = y * (z / a)
	elif a <= -1.56e-21:
		tmp = x
	elif a <= 1.4e-67:
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+112)
		tmp = x;
	elseif (a <= -5e+45)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -1.56e-21)
		tmp = x;
	elseif (a <= 1.4e-67)
		tmp = Float64(z * 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 <= -9.5e+112)
		tmp = x;
	elseif (a <= -5e+45)
		tmp = y * (z / a);
	elseif (a <= -1.56e-21)
		tmp = x;
	elseif (a <= 1.4e-67)
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+112], x, If[LessEqual[a, -5e+45], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.56e-21], x, If[LessEqual[a, 1.4e-67], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000008e112 or -5e45 < a < -1.55999999999999999e-21 or 1.40000000000000005e-67 < a

   1. Initial program 87.1%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 56.9%

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

   if -9.5000000000000008e112 < a < -5e45

   1. Initial program 84.2%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around 0 51.2%

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

      1. +-commutative 51.2%

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

      2. associate-*l/ 58.8%

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

      3. *-commutative 58.8%

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

      4. fma-def 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around inf 43.0%

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

      1. associate-*r/ 50.8%

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

   10. Simplified 50.8%

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

   if -1.55999999999999999e-21 < a < 1.40000000000000005e-67

   1. Initial program 99.3%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around 0 66.4%

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

      1. +-commutative 66.4%

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

      2. associate-*l/ 68.3%

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

      3. *-commutative 68.3%

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

      4. fma-def 68.3%

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

   7. Simplified 68.3%

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

   8. Taylor expanded in z around inf 50.4%

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

      1. associate-*l/ 52.4%

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

   10. Simplified 52.4%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.56 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+118} \lor \neg \left(t \leq 4.1 \cdot 10^{-13}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+118) (not (<= t 4.1e-13)))
   (- x (* y (/ t a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+118) || !(t <= 4.1e-13)) {
		tmp = x - (y * (t / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.2d+118)) .or. (.not. (t <= 4.1d-13))) then
        tmp = x - (y * (t / a))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+118) || !(t <= 4.1e-13)) {
		tmp = x - (y * (t / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e+118) or not (t <= 4.1e-13):
		tmp = x - (y * (t / a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+118) || !(t <= 4.1e-13))
		tmp = Float64(x - Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e+118) || ~((t <= 4.1e-13)))
		tmp = x - (y * (t / a));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e+118], N[Not[LessEqual[t, 4.1e-13]], $MachinePrecision]], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e118 or 4.1000000000000002e-13 < t

   1. Initial program 86.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

      3. unsub-neg 89.4%

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

      4. associate-*r/ 81.7%

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

      5. associate-/l* 88.5%

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

      6. associate-/r/ 87.2%

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

   7. Simplified 87.2%

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

   if -1.2e118 < t < 4.1000000000000002e-13

   1. Initial program 95.3%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+118} \lor \neg \left(t \leq 4.1 \cdot 10^{-13}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 4.6 \cdot 10^{-12}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+118) (not (<= t 4.6e-12)))
   (- x (/ t (/ a y)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+118) || !(t <= 4.6e-12)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d+118)) .or. (.not. (t <= 4.6d-12))) then
        tmp = x - (t / (a / y))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+118) || !(t <= 4.6e-12)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+118) or not (t <= 4.6e-12):
		tmp = x - (t / (a / y))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+118) || !(t <= 4.6e-12))
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+118) || ~((t <= 4.6e-12)))
		tmp = x - (t / (a / y));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+118], N[Not[LessEqual[t, 4.6e-12]], $MachinePrecision]], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e118 or 4.59999999999999979e-12 < t

   1. Initial program 86.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

      3. unsub-neg 89.4%

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

      4. associate-*r/ 81.7%

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

      5. associate-/l* 88.5%

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

      6. associate-/r/ 87.2%

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

   7. Simplified 87.2%

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

      1. associate-*l/ 81.7%

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

      2. associate-/l* 88.5%

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

   9. Applied egg-rr 88.5%

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

   if -1.05e118 < t < 4.59999999999999979e-12

   1. Initial program 95.3%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 4.6 \cdot 10^{-12}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+118} \lor \neg \left(t \leq 2.35 \cdot 10^{-12}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.1e+118) (not (<= t 2.35e-12)))
   (- x (* t (/ y a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+118) || !(t <= 2.35e-12)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.1d+118)) .or. (.not. (t <= 2.35d-12))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+118) || !(t <= 2.35e-12)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.1e+118) or not (t <= 2.35e-12):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.1e+118) || !(t <= 2.35e-12))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.1e+118) || ~((t <= 2.35e-12)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.1e+118], N[Not[LessEqual[t, 2.35e-12]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.09999999999999993e118 or 2.34999999999999988e-12 < t

   1. Initial program 86.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

      3. distribute-rgt-neg-in 89.4%

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

   7. Simplified 89.4%

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

   if -1.09999999999999993e118 < t < 2.34999999999999988e-12

   1. Initial program 95.3%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+118} \lor \neg \left(t \leq 2.35 \cdot 10^{-12}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+72} \lor \neg \left(y \leq 3.7 \cdot 10^{+96}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.25e+72) (not (<= y 3.7e+96))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.25e+72) || !(y <= 3.7e+96)) {
		tmp = y * (z / 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 ((y <= (-1.25d+72)) .or. (.not. (y <= 3.7d+96))) then
        tmp = y * (z / 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 ((y <= -1.25e+72) || !(y <= 3.7e+96)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.25e+72) or not (y <= 3.7e+96):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.25e+72) || !(y <= 3.7e+96))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.25e+72) || ~((y <= 3.7e+96)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.25e+72], N[Not[LessEqual[y, 3.7e+96]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999998e72 or 3.69999999999999991e96 < y

   1. Initial program 82.4%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around 0 55.3%

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

      1. +-commutative 55.3%

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

      2. associate-*l/ 65.1%

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

      3. *-commutative 65.1%

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

      4. fma-def 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in z around inf 44.7%

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

      1. associate-*r/ 49.5%

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

   10. Simplified 49.5%

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

   if -1.24999999999999998e72 < y < 3.69999999999999991e96

   1. Initial program 97.8%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around inf 53.2%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+72} \lor \neg \left(y \leq 3.7 \cdot 10^{+96}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 93.5% 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 91.9%

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

   1. associate-/l* 92.9%

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

3. Simplified 92.9%

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

5. Final simplification 92.9%

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

Alternative 13: 97.1% 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 91.9%

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

   1. *-commutative 91.9%

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

   2. associate-/l* 96.6%

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

3. Simplified 96.6%

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

5. Final simplification 96.6%

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

Alternative 14: 39.8% 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 91.9%

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

   1. associate-/l* 92.9%

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

3. Simplified 92.9%

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

5. Taylor expanded in x around inf 38.5%

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

6. Final simplification 38.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024019 
(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)))