Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, I

Percentage Accurate: 91.2% → 94.9%

Time: 8.5s

Alternatives: 18

Speedup: 0.5×

• 28.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+179}\right):\\ \;\;\;\;y \cdot \mathsf{fma}\left(-4.5, t \cdot \frac{z}{y \cdot a}, 0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) (- INFINITY)) (not (<= (* x y) 5e+179)))
   (* y (fma -4.5 (* t (/ z (* y a))) (* 0.5 (/ x a))))
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -((double) INFINITY)) || !((x * y) <= 5e+179)) {
		tmp = y * fma(-4.5, (t * (z / (y * a))), (0.5 * (x / a)));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= Float64(-Inf)) || !(Float64(x * y) <= 5e+179))
		tmp = Float64(y * fma(-4.5, Float64(t * Float64(z / Float64(y * a))), Float64(0.5 * Float64(x / a))));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+179]], $MachinePrecision]], N[(y * N[(-4.5 * N[(t * N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0 or 5e179 < (*.f64 x y)

   1. Initial program 66.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 93.0%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. fma-define 93.0%

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a \cdot y}, 0.5 \cdot \frac{x}{a}\right)} \]

      2. associate-/l* 97.7%

         \[\leadsto y \cdot \mathsf{fma}\left(-4.5, \color{blue}{t \cdot \frac{z}{a \cdot y}}, 0.5 \cdot \frac{x}{a}\right) \]

   5. Simplified 97.7%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a \cdot y}, 0.5 \cdot \frac{x}{a}\right)} \]

   if -inf.0 < (*.f64 x y) < 5e179

   1. Initial program 97.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. div-sub 95.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      2. *-commutative 95.1%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 97.0%

         \[\leadsto \color{blue}{\frac{y \cdot x - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. cancel-sign-sub-inv 97.0%

         \[\leadsto \frac{\color{blue}{y \cdot x + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      5. *-commutative 97.0%

         \[\leadsto \frac{\color{blue}{x \cdot y} + \left(-z \cdot 9\right) \cdot t}{a \cdot 2} \]

      6. fma-define 97.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      7. distribute-rgt-neg-in 97.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      8. associate-*r* 97.1%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      9. distribute-lft-neg-in 97.1%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      10. *-commutative 97.1%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      11. distribute-rgt-neg-in 97.1%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      12. metadata-eval 97.1%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+179}\right):\\ \;\;\;\;y \cdot \mathsf{fma}\left(-4.5, t \cdot \frac{z}{y \cdot a}, 0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+179}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) 5e+179)
     (/ (fma x y (* z (* t -9.0))) (* a 2.0))
     (* y (* 0.5 (/ x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 5e+179) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = y * (0.5 * (x / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= 5e+179)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+179], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 49.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 55.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 55.5%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 93.9%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 93.9%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 93.9%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 93.9%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 93.9%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -inf.0 < (*.f64 x y) < 5e179

   1. Initial program 97.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. div-sub 95.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      2. *-commutative 95.1%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 97.0%

         \[\leadsto \color{blue}{\frac{y \cdot x - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. cancel-sign-sub-inv 97.0%

         \[\leadsto \frac{\color{blue}{y \cdot x + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      5. *-commutative 97.0%

         \[\leadsto \frac{\color{blue}{x \cdot y} + \left(-z \cdot 9\right) \cdot t}{a \cdot 2} \]

      6. fma-define 97.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      7. distribute-rgt-neg-in 97.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      8. associate-*r* 97.1%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      9. distribute-lft-neg-in 97.1%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      10. *-commutative 97.1%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      11. distribute-rgt-neg-in 97.1%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      12. metadata-eval 97.1%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   if 5e179 < (*.f64 x y)

   1. Initial program 78.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.2%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 96.3%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+179}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;-4.5 \cdot \left(\frac{1}{a} \cdot \frac{t}{\frac{1}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-39)
   (/ (* y 0.5) (/ a x))
   (if (<= (* x y) 1e-93)
     (* z (/ (* -4.5 t) a))
     (if (<= (* x y) 5e-27)
       (/ (* x y) (* a 2.0))
       (if (<= (* x y) 2000000000.0)
         (* -4.5 (* (/ 1.0 a) (/ t (/ 1.0 z))))
         (* x (/ (* y 0.5) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-39) {
		tmp = (y * 0.5) / (a / x);
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 2000000000.0) {
		tmp = -4.5 * ((1.0 / a) * (t / (1.0 / z)));
	} else {
		tmp = x * ((y * 0.5) / 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 ((x * y) <= (-2d-39)) then
        tmp = (y * 0.5d0) / (a / x)
    else if ((x * y) <= 1d-93) then
        tmp = z * (((-4.5d0) * t) / a)
    else if ((x * y) <= 5d-27) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 2000000000.0d0) then
        tmp = (-4.5d0) * ((1.0d0 / a) * (t / (1.0d0 / z)))
    else
        tmp = x * ((y * 0.5d0) / 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 ((x * y) <= -2e-39) {
		tmp = (y * 0.5) / (a / x);
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 2000000000.0) {
		tmp = -4.5 * ((1.0 / a) * (t / (1.0 / z)));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-39:
		tmp = (y * 0.5) / (a / x)
	elif (x * y) <= 1e-93:
		tmp = z * ((-4.5 * t) / a)
	elif (x * y) <= 5e-27:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 2000000000.0:
		tmp = -4.5 * ((1.0 / a) * (t / (1.0 / z)))
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-39)
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	elseif (Float64(x * y) <= 1e-93)
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 2000000000.0)
		tmp = Float64(-4.5 * Float64(Float64(1.0 / a) * Float64(t / Float64(1.0 / z))));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-39)
		tmp = (y * 0.5) / (a / x);
	elseif ((x * y) <= 1e-93)
		tmp = z * ((-4.5 * t) / a);
	elseif ((x * y) <= 5e-27)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 2000000000.0)
		tmp = -4.5 * ((1.0 / a) * (t / (1.0 / z)));
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-39], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-93], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0], N[(-4.5 * N[(N[(1.0 / a), $MachinePrecision] * N[(t / N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999986e-39

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.9%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 68.9%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{x}{a}} \]

      2. metadata-eval 68.9%

         \[\leadsto \left(y \cdot \color{blue}{\frac{1}{2}}\right) \cdot \frac{x}{a} \]

      3. div-inv 68.9%

         \[\leadsto \color{blue}{\frac{y}{2}} \cdot \frac{x}{a} \]

      4. clear-num 68.8%

         \[\leadsto \frac{y}{2} \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      5. un-div-inv 69.3%

         \[\leadsto \color{blue}{\frac{\frac{y}{2}}{\frac{a}{x}}} \]

      6. div-inv 69.3%

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{2}}}{\frac{a}{x}} \]

      7. metadata-eval 69.3%

         \[\leadsto \frac{y \cdot \color{blue}{0.5}}{\frac{a}{x}} \]

   6. Applied egg-rr 69.3%

      \[\leadsto \color{blue}{\frac{y \cdot 0.5}{\frac{a}{x}}} \]

   if -1.99999999999999986e-39 < (*.f64 x y) < 9.999999999999999e-94

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 78.4%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 80.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 80.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 80.9%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 80.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   if 9.999999999999999e-94 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]

   if 5.0000000000000002e-27 < (*.f64 x y) < 2e9

   1. Initial program 100.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.9%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 85.9%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. clear-num 85.9%

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{1}{\frac{a}{z}}}\right) \]

      2. un-div-inv 85.7%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Applied egg-rr 85.7%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. *-un-lft-identity 85.7%

         \[\leadsto -4.5 \cdot \frac{\color{blue}{1 \cdot t}}{\frac{a}{z}} \]

      2. div-inv 85.7%

         \[\leadsto -4.5 \cdot \frac{1 \cdot t}{\color{blue}{a \cdot \frac{1}{z}}} \]

      3. times-frac 85.9%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{1}{a} \cdot \frac{t}{\frac{1}{z}}\right)} \]

   9. Applied egg-rr 85.9%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{1}{a} \cdot \frac{t}{\frac{1}{z}}\right)} \]

   if 2e9 < (*.f64 x y)

   1. Initial program 89.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 89.7%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 89.7%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 89.7%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 89.7%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 89.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 89.7%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      3. associate-*r/ 72.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      4. associate-*l* 77.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      5. associate-*r/ 77.6%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   9. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-39)
   (/ (* y 0.5) (/ a x))
   (if (<= (* x y) 1e-93)
     (* z (/ (* -4.5 t) a))
     (if (<= (* x y) 5e-27)
       (/ (* x y) (* a 2.0))
       (if (<= (* x y) 2000000000.0)
         (/ (* z (* t -9.0)) (* a 2.0))
         (* x (/ (* y 0.5) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-39) {
		tmp = (y * 0.5) / (a / x);
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (z * (t * -9.0)) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / 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 ((x * y) <= (-2d-39)) then
        tmp = (y * 0.5d0) / (a / x)
    else if ((x * y) <= 1d-93) then
        tmp = z * (((-4.5d0) * t) / a)
    else if ((x * y) <= 5d-27) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 2000000000.0d0) then
        tmp = (z * (t * (-9.0d0))) / (a * 2.0d0)
    else
        tmp = x * ((y * 0.5d0) / 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 ((x * y) <= -2e-39) {
		tmp = (y * 0.5) / (a / x);
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (z * (t * -9.0)) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-39:
		tmp = (y * 0.5) / (a / x)
	elif (x * y) <= 1e-93:
		tmp = z * ((-4.5 * t) / a)
	elif (x * y) <= 5e-27:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 2000000000.0:
		tmp = (z * (t * -9.0)) / (a * 2.0)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-39)
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	elseif (Float64(x * y) <= 1e-93)
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 2000000000.0)
		tmp = Float64(Float64(z * Float64(t * -9.0)) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-39)
		tmp = (y * 0.5) / (a / x);
	elseif ((x * y) <= 1e-93)
		tmp = z * ((-4.5 * t) / a);
	elseif ((x * y) <= 5e-27)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 2000000000.0)
		tmp = (z * (t * -9.0)) / (a * 2.0);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-39], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-93], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0], N[(N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999986e-39

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.9%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 68.9%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{x}{a}} \]

      2. metadata-eval 68.9%

         \[\leadsto \left(y \cdot \color{blue}{\frac{1}{2}}\right) \cdot \frac{x}{a} \]

      3. div-inv 68.9%

         \[\leadsto \color{blue}{\frac{y}{2}} \cdot \frac{x}{a} \]

      4. clear-num 68.8%

         \[\leadsto \frac{y}{2} \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      5. un-div-inv 69.3%

         \[\leadsto \color{blue}{\frac{\frac{y}{2}}{\frac{a}{x}}} \]

      6. div-inv 69.3%

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{2}}}{\frac{a}{x}} \]

      7. metadata-eval 69.3%

         \[\leadsto \frac{y \cdot \color{blue}{0.5}}{\frac{a}{x}} \]

   6. Applied egg-rr 69.3%

      \[\leadsto \color{blue}{\frac{y \cdot 0.5}{\frac{a}{x}}} \]

   if -1.99999999999999986e-39 < (*.f64 x y) < 9.999999999999999e-94

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 78.4%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 80.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 80.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 80.9%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 80.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   if 9.999999999999999e-94 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]

   if 5.0000000000000002e-27 < (*.f64 x y) < 2e9

   1. Initial program 100.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.9%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left(t \cdot z\right)}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 85.9%

         \[\leadsto \frac{\color{blue}{\left(t \cdot z\right) \cdot -9}}{a \cdot 2} \]

      2. *-commutative 85.9%

         \[\leadsto \frac{\color{blue}{\left(z \cdot t\right)} \cdot -9}{a \cdot 2} \]

      3. associate-*r* 85.9%

         \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]

   5. Simplified 85.9%

      \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]

   if 2e9 < (*.f64 x y)

   1. Initial program 89.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 89.7%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 89.7%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 89.7%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 89.7%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 89.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 89.7%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      3. associate-*r/ 72.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      4. associate-*l* 77.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      5. associate-*r/ 77.6%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   9. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-39)
   (/ (* y 0.5) (/ a x))
   (if (<= (* x y) 1e-93)
     (* z (/ (* -4.5 t) a))
     (if (<= (* x y) 5e-27)
       (/ (* x y) (* a 2.0))
       (if (<= (* x y) 2000000000.0)
         (/ (* -4.5 t) (/ a z))
         (* x (/ (* y 0.5) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-39) {
		tmp = (y * 0.5) / (a / x);
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (-4.5 * t) / (a / z);
	} else {
		tmp = x * ((y * 0.5) / 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 ((x * y) <= (-2d-39)) then
        tmp = (y * 0.5d0) / (a / x)
    else if ((x * y) <= 1d-93) then
        tmp = z * (((-4.5d0) * t) / a)
    else if ((x * y) <= 5d-27) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 2000000000.0d0) then
        tmp = ((-4.5d0) * t) / (a / z)
    else
        tmp = x * ((y * 0.5d0) / 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 ((x * y) <= -2e-39) {
		tmp = (y * 0.5) / (a / x);
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (-4.5 * t) / (a / z);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-39:
		tmp = (y * 0.5) / (a / x)
	elif (x * y) <= 1e-93:
		tmp = z * ((-4.5 * t) / a)
	elif (x * y) <= 5e-27:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 2000000000.0:
		tmp = (-4.5 * t) / (a / z)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-39)
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	elseif (Float64(x * y) <= 1e-93)
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 2000000000.0)
		tmp = Float64(Float64(-4.5 * t) / Float64(a / z));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-39)
		tmp = (y * 0.5) / (a / x);
	elseif ((x * y) <= 1e-93)
		tmp = z * ((-4.5 * t) / a);
	elseif ((x * y) <= 5e-27)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 2000000000.0)
		tmp = (-4.5 * t) / (a / z);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-39], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-93], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0], N[(N[(-4.5 * t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999986e-39

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.9%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 68.9%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \frac{x}{a}} \]

      2. metadata-eval 68.9%

         \[\leadsto \left(y \cdot \color{blue}{\frac{1}{2}}\right) \cdot \frac{x}{a} \]

      3. div-inv 68.9%

         \[\leadsto \color{blue}{\frac{y}{2}} \cdot \frac{x}{a} \]

      4. clear-num 68.8%

         \[\leadsto \frac{y}{2} \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      5. un-div-inv 69.3%

         \[\leadsto \color{blue}{\frac{\frac{y}{2}}{\frac{a}{x}}} \]

      6. div-inv 69.3%

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{2}}}{\frac{a}{x}} \]

      7. metadata-eval 69.3%

         \[\leadsto \frac{y \cdot \color{blue}{0.5}}{\frac{a}{x}} \]

   6. Applied egg-rr 69.3%

      \[\leadsto \color{blue}{\frac{y \cdot 0.5}{\frac{a}{x}}} \]

   if -1.99999999999999986e-39 < (*.f64 x y) < 9.999999999999999e-94

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 78.4%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 80.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 80.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 80.9%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 80.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   if 9.999999999999999e-94 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]

   if 5.0000000000000002e-27 < (*.f64 x y) < 2e9

   1. Initial program 100.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.9%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 85.9%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 85.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot t\right) \cdot \frac{z}{a}} \]

      2. clear-num 85.9%

         \[\leadsto \left(-4.5 \cdot t\right) \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      3. un-div-inv 85.7%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]

      4. *-commutative 85.7%

         \[\leadsto \frac{\color{blue}{t \cdot -4.5}}{\frac{a}{z}} \]

   7. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{t \cdot -4.5}{\frac{a}{z}}} \]

   if 2e9 < (*.f64 x y)

   1. Initial program 89.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 89.7%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 89.7%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 89.7%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 89.7%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 89.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 89.7%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      3. associate-*r/ 72.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      4. associate-*l* 77.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      5. associate-*r/ 77.6%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   9. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-39)
   (* y (* 0.5 (/ x a)))
   (if (<= (* x y) 1e-93)
     (* z (/ (* -4.5 t) a))
     (if (<= (* x y) 5e-27)
       (/ (* x y) (* a 2.0))
       (if (<= (* x y) 2000000000.0)
         (/ (* -4.5 t) (/ a z))
         (* x (/ (* y 0.5) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-39) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (-4.5 * t) / (a / z);
	} else {
		tmp = x * ((y * 0.5) / 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 ((x * y) <= (-2d-39)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 1d-93) then
        tmp = z * (((-4.5d0) * t) / a)
    else if ((x * y) <= 5d-27) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 2000000000.0d0) then
        tmp = ((-4.5d0) * t) / (a / z)
    else
        tmp = x * ((y * 0.5d0) / 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 ((x * y) <= -2e-39) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (-4.5 * t) / (a / z);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-39:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 1e-93:
		tmp = z * ((-4.5 * t) / a)
	elif (x * y) <= 5e-27:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 2000000000.0:
		tmp = (-4.5 * t) / (a / z)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-39)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 1e-93)
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 2000000000.0)
		tmp = Float64(Float64(-4.5 * t) / Float64(a / z));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-39)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 1e-93)
		tmp = z * ((-4.5 * t) / a);
	elseif ((x * y) <= 5e-27)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 2000000000.0)
		tmp = (-4.5 * t) / (a / z);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-39], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-93], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0], N[(N[(-4.5 * t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999986e-39

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.9%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]

   if -1.99999999999999986e-39 < (*.f64 x y) < 9.999999999999999e-94

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 78.4%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 80.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 80.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 80.9%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 80.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   if 9.999999999999999e-94 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]

   if 5.0000000000000002e-27 < (*.f64 x y) < 2e9

   1. Initial program 100.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.9%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 85.9%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 85.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot t\right) \cdot \frac{z}{a}} \]

      2. clear-num 85.9%

         \[\leadsto \left(-4.5 \cdot t\right) \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      3. un-div-inv 85.7%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]

      4. *-commutative 85.7%

         \[\leadsto \frac{\color{blue}{t \cdot -4.5}}{\frac{a}{z}} \]

   7. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{t \cdot -4.5}{\frac{a}{z}}} \]

   if 2e9 < (*.f64 x y)

   1. Initial program 89.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 89.7%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 89.7%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 89.7%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 89.7%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 89.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 89.7%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      3. associate-*r/ 72.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      4. associate-*l* 77.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      5. associate-*r/ 77.6%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   9. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-39)
   (* y (* 0.5 (/ x a)))
   (if (<= (* x y) 1e-93)
     (* z (/ (* -4.5 t) a))
     (if (<= (* x y) 5e-27)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 2000000000.0)
         (/ (* -4.5 t) (/ a z))
         (* x (/ (* y 0.5) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-39) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (-4.5 * t) / (a / z);
	} else {
		tmp = x * ((y * 0.5) / 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 ((x * y) <= (-2d-39)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 1d-93) then
        tmp = z * (((-4.5d0) * t) / a)
    else if ((x * y) <= 5d-27) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 2000000000.0d0) then
        tmp = ((-4.5d0) * t) / (a / z)
    else
        tmp = x * ((y * 0.5d0) / 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 ((x * y) <= -2e-39) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (-4.5 * t) / (a / z);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-39:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 1e-93:
		tmp = z * ((-4.5 * t) / a)
	elif (x * y) <= 5e-27:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 2000000000.0:
		tmp = (-4.5 * t) / (a / z)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-39)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 1e-93)
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 2000000000.0)
		tmp = Float64(Float64(-4.5 * t) / Float64(a / z));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-39)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 1e-93)
		tmp = z * ((-4.5 * t) / a);
	elseif ((x * y) <= 5e-27)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 2000000000.0)
		tmp = (-4.5 * t) / (a / z);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-39], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-93], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0], N[(N[(-4.5 * t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999986e-39

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.9%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]

   if -1.99999999999999986e-39 < (*.f64 x y) < 9.999999999999999e-94

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 78.4%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 80.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 80.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 80.9%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 80.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   if 9.999999999999999e-94 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. clear-num 63.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y}}} \]

      2. associate-/r/ 65.0%

         \[\leadsto \color{blue}{\frac{1}{a \cdot 2} \cdot \left(x \cdot y\right)} \]

      3. *-commutative 65.0%

         \[\leadsto \frac{1}{\color{blue}{2 \cdot a}} \cdot \left(x \cdot y\right) \]

      4. associate-/r* 65.0%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{a}} \cdot \left(x \cdot y\right) \]

      5. metadata-eval 65.0%

         \[\leadsto \frac{\color{blue}{0.5}}{a} \cdot \left(x \cdot y\right) \]

   5. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

   if 5.0000000000000002e-27 < (*.f64 x y) < 2e9

   1. Initial program 100.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.9%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 85.9%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 85.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot t\right) \cdot \frac{z}{a}} \]

      2. clear-num 85.9%

         \[\leadsto \left(-4.5 \cdot t\right) \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      3. un-div-inv 85.7%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]

      4. *-commutative 85.7%

         \[\leadsto \frac{\color{blue}{t \cdot -4.5}}{\frac{a}{z}} \]

   7. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{t \cdot -4.5}{\frac{a}{z}}} \]

   if 2e9 < (*.f64 x y)

   1. Initial program 89.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 89.7%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 89.7%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 89.7%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 89.7%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 89.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 89.7%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      3. associate-*r/ 72.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      4. associate-*l* 77.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      5. associate-*r/ 77.6%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   9. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-39)
   (* y (* 0.5 (/ x a)))
   (if (<= (* x y) 1e-93)
     (* z (/ (* -4.5 t) a))
     (if (<= (* x y) 5e-27)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 2000000000.0)
         (* (/ t a) (* -4.5 z))
         (* x (/ (* y 0.5) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-39) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (t / a) * (-4.5 * z);
	} else {
		tmp = x * ((y * 0.5) / 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 ((x * y) <= (-2d-39)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 1d-93) then
        tmp = z * (((-4.5d0) * t) / a)
    else if ((x * y) <= 5d-27) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 2000000000.0d0) then
        tmp = (t / a) * ((-4.5d0) * z)
    else
        tmp = x * ((y * 0.5d0) / 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 ((x * y) <= -2e-39) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 1e-93) {
		tmp = z * ((-4.5 * t) / a);
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 2000000000.0) {
		tmp = (t / a) * (-4.5 * z);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-39:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 1e-93:
		tmp = z * ((-4.5 * t) / a)
	elif (x * y) <= 5e-27:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 2000000000.0:
		tmp = (t / a) * (-4.5 * z)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-39)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 1e-93)
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 2000000000.0)
		tmp = Float64(Float64(t / a) * Float64(-4.5 * z));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-39)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 1e-93)
		tmp = z * ((-4.5 * t) / a);
	elseif ((x * y) <= 5e-27)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 2000000000.0)
		tmp = (t / a) * (-4.5 * z);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-39], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-93], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0], N[(N[(t / a), $MachinePrecision] * N[(-4.5 * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999986e-39

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.9%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]

   if -1.99999999999999986e-39 < (*.f64 x y) < 9.999999999999999e-94

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 78.4%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 80.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 80.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 80.9%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 80.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   if 9.999999999999999e-94 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. clear-num 63.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y}}} \]

      2. associate-/r/ 65.0%

         \[\leadsto \color{blue}{\frac{1}{a \cdot 2} \cdot \left(x \cdot y\right)} \]

      3. *-commutative 65.0%

         \[\leadsto \frac{1}{\color{blue}{2 \cdot a}} \cdot \left(x \cdot y\right) \]

      4. associate-/r* 65.0%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{a}} \cdot \left(x \cdot y\right) \]

      5. metadata-eval 65.0%

         \[\leadsto \frac{\color{blue}{0.5}}{a} \cdot \left(x \cdot y\right) \]

   5. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

   if 5.0000000000000002e-27 < (*.f64 x y) < 2e9

   1. Initial program 100.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 85.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 85.9%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 85.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 85.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 85.9%

         \[\leadsto \color{blue}{\left(\frac{t}{a} \cdot -4.5\right)} \cdot z \]

      6. associate-*l* 85.9%

         \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(-4.5 \cdot z\right)} \]

   5. Simplified 85.9%

      \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(-4.5 \cdot z\right)} \]

   if 2e9 < (*.f64 x y)

   1. Initial program 89.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 89.7%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 89.7%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 89.7%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 89.7%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 89.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 89.7%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      3. associate-*r/ 72.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      4. associate-*l* 77.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      5. associate-*r/ 77.6%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   9. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;\frac{t}{a} \cdot \left(-4.5 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (* -4.5 t) a))))
   (if (<= (* x y) -2e-39)
     (* y (* 0.5 (/ x a)))
     (if (<= (* x y) 1e-93)
       t_1
       (if (<= (* x y) 5e-27)
         (* (* x y) (/ 0.5 a))
         (if (<= (* x y) 2000000000.0) t_1 (* x (/ (* y 0.5) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((-4.5 * t) / a);
	double tmp;
	if ((x * y) <= -2e-39) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 1e-93) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 2000000000.0) {
		tmp = t_1;
	} else {
		tmp = x * ((y * 0.5) / 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) :: tmp
    t_1 = z * (((-4.5d0) * t) / a)
    if ((x * y) <= (-2d-39)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 1d-93) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 2000000000.0d0) then
        tmp = t_1
    else
        tmp = x * ((y * 0.5d0) / 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 = z * ((-4.5 * t) / a);
	double tmp;
	if ((x * y) <= -2e-39) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 1e-93) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 2000000000.0) {
		tmp = t_1;
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((-4.5 * t) / a)
	tmp = 0
	if (x * y) <= -2e-39:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 1e-93:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 2000000000.0:
		tmp = t_1
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-4.5 * t) / a))
	tmp = 0.0
	if (Float64(x * y) <= -2e-39)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 1e-93)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 2000000000.0)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((-4.5 * t) / a);
	tmp = 0.0;
	if ((x * y) <= -2e-39)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 1e-93)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 2000000000.0)
		tmp = t_1;
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e-39], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-93], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0], t$95$1, N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999986e-39

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.9%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]

   if -1.99999999999999986e-39 < (*.f64 x y) < 9.999999999999999e-94 or 5.0000000000000002e-27 < (*.f64 x y) < 2e9

   1. Initial program 95.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.8%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 78.9%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 81.2%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 81.2%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 81.2%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 81.2%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   if 9.999999999999999e-94 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. clear-num 63.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y}}} \]

      2. associate-/r/ 65.0%

         \[\leadsto \color{blue}{\frac{1}{a \cdot 2} \cdot \left(x \cdot y\right)} \]

      3. *-commutative 65.0%

         \[\leadsto \frac{1}{\color{blue}{2 \cdot a}} \cdot \left(x \cdot y\right) \]

      4. associate-/r* 65.0%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{a}} \cdot \left(x \cdot y\right) \]

      5. metadata-eval 65.0%

         \[\leadsto \frac{\color{blue}{0.5}}{a} \cdot \left(x \cdot y\right) \]

   5. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y\right)} \]

   if 2e9 < (*.f64 x y)

   1. Initial program 89.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 89.7%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 89.7%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 89.7%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 89.7%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 89.7%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 89.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 89.7%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 89.7%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 89.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      3. associate-*r/ 72.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      4. associate-*l* 77.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      5. associate-*r/ 77.6%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   9. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-93}:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2000000000:\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+179}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) 5e+179)
     (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))
     (* y (* 0.5 (/ x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 5e+179) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = y * (0.5 * (x / a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 5e+179) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = y * (0.5 * (x / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = x * ((y * 0.5) / a)
	elif (x * y) <= 5e+179:
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0)
	else:
		tmp = y * (0.5 * (x / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= 5e+179)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = x * ((y * 0.5) / a);
	elseif ((x * y) <= 5e+179)
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	else
		tmp = y * (0.5 * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+179], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 49.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 55.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 55.5%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 93.9%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 93.9%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 93.9%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 93.9%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 93.9%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -inf.0 < (*.f64 x y) < 5e179

   1. Initial program 97.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   if 5e179 < (*.f64 x y)

   1. Initial program 78.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.2%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 96.3%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+179}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+179}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) 5e+179)
     (/ 0.5 (/ a (+ (* x y) (* -9.0 (* t z)))))
     (* y (* 0.5 (/ x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 5e+179) {
		tmp = 0.5 / (a / ((x * y) + (-9.0 * (t * z))));
	} else {
		tmp = y * (0.5 * (x / a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 5e+179) {
		tmp = 0.5 / (a / ((x * y) + (-9.0 * (t * z))));
	} else {
		tmp = y * (0.5 * (x / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = x * ((y * 0.5) / a)
	elif (x * y) <= 5e+179:
		tmp = 0.5 / (a / ((x * y) + (-9.0 * (t * z))))
	else:
		tmp = y * (0.5 * (x / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= 5e+179)
		tmp = Float64(0.5 / Float64(a / Float64(Float64(x * y) + Float64(-9.0 * Float64(t * z)))));
	else
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = x * ((y * 0.5) / a);
	elseif ((x * y) <= 5e+179)
		tmp = 0.5 / (a / ((x * y) + (-9.0 * (t * z))));
	else
		tmp = y * (0.5 * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+179], N[(0.5 / N[(a / N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 49.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 55.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 55.5%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 93.9%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 93.9%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 93.9%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 93.9%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 93.9%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -inf.0 < (*.f64 x y) < 5e179

   1. Initial program 97.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 96.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 96.5%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 96.5%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 96.5%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 96.5%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 96.5%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 96.5%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 96.5%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 96.5%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 96.5%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 96.5%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 96.5%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 96.6%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 96.6%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 96.6%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 96.6%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 96.6%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 96.6%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 96.6%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 96.6%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 96.6%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in a around 0 96.6%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{a}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}} \]

   if 5e179 < (*.f64 x y)

   1. Initial program 78.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.2%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 96.3%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+179}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-147} \lor \neg \left(t \leq 1.35 \cdot 10^{+26}\right):\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.95e-147) (not (<= t 1.35e+26)))
   (* z (/ (* -4.5 t) a))
   (* y (* 0.5 (/ x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.95e-147) || !(t <= 1.35e+26)) {
		tmp = z * ((-4.5 * t) / a);
	} else {
		tmp = y * (0.5 * (x / 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 <= (-1.95d-147)) .or. (.not. (t <= 1.35d+26))) then
        tmp = z * (((-4.5d0) * t) / a)
    else
        tmp = y * (0.5d0 * (x / 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 <= -1.95e-147) || !(t <= 1.35e+26)) {
		tmp = z * ((-4.5 * t) / a);
	} else {
		tmp = y * (0.5 * (x / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.95e-147) or not (t <= 1.35e+26):
		tmp = z * ((-4.5 * t) / a)
	else:
		tmp = y * (0.5 * (x / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.95e-147) || !(t <= 1.35e+26))
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	else
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.95e-147) || ~((t <= 1.35e+26)))
		tmp = z * ((-4.5 * t) / a);
	else
		tmp = y * (0.5 * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.95e-147], N[Not[LessEqual[t, 1.35e+26]], $MachinePrecision]], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9499999999999999e-147 or 1.35e26 < t

   1. Initial program 90.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 57.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 57.7%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 57.8%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 58.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 58.9%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 58.9%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 58.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   if -1.9499999999999999e-147 < t < 1.35e26

   1. Initial program 94.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.4%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.3%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-147} \lor \neg \left(t \leq 1.35 \cdot 10^{+26}\right):\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-147}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e-147)
   (* -4.5 (/ (* t z) a))
   (if (<= t 1.35e+26) (* y (* 0.5 (/ x a))) (* -4.5 (/ t (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e-147) {
		tmp = -4.5 * ((t * z) / a);
	} else if (t <= 1.35e+26) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.95d-147)) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (t <= 1.35d+26) then
        tmp = y * (0.5d0 * (x / a))
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e-147) {
		tmp = -4.5 * ((t * z) / a);
	} else if (t <= 1.35e+26) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e-147:
		tmp = -4.5 * ((t * z) / a)
	elif t <= 1.35e+26:
		tmp = y * (0.5 * (x / a))
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e-147)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (t <= 1.35e+26)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e-147)
		tmp = -4.5 * ((t * z) / a);
	elseif (t <= 1.35e+26)
		tmp = y * (0.5 * (x / a));
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e-147], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+26], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9499999999999999e-147

   1. Initial program 90.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 54.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if -1.9499999999999999e-147 < t < 1.35e26

   1. Initial program 94.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.4%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   4. Taylor expanded in t around 0 68.3%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{a}\right)} \]

   if 1.35e26 < t

   1. Initial program 90.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.8%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 65.3%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. clear-num 65.3%

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{1}{\frac{a}{z}}}\right) \]

      2. un-div-inv 65.4%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Applied egg-rr 65.4%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-147}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e-147)
   (* -4.5 (/ (* t z) a))
   (if (<= t 1.35e+26) (* x (/ (* y 0.5) a)) (* -4.5 (/ t (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e-147) {
		tmp = -4.5 * ((t * z) / a);
	} else if (t <= 1.35e+26) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.95d-147)) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (t <= 1.35d+26) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e-147) {
		tmp = -4.5 * ((t * z) / a);
	} else if (t <= 1.35e+26) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e-147:
		tmp = -4.5 * ((t * z) / a)
	elif t <= 1.35e+26:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e-147)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (t <= 1.35e+26)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e-147)
		tmp = -4.5 * ((t * z) / a);
	elseif (t <= 1.35e+26)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e-147], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+26], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9499999999999999e-147

   1. Initial program 90.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 54.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if -1.9499999999999999e-147 < t < 1.35e26

   1. Initial program 94.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 94.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 94.1%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 94.1%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 94.1%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 94.1%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 94.1%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 94.1%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 94.1%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 94.1%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 94.1%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 94.1%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 94.1%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

      4. associate-*r* 94.3%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot z\right) \cdot -9}\right)}} \]

      5. *-commutative 94.3%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      6. metadata-eval 94.3%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)\right)}} \]

      7. distribute-lft-neg-in 94.3%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9 \cdot \left(t \cdot z\right)}\right)}} \]

      8. distribute-lft-neg-in 94.3%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(t \cdot z\right)}\right)}} \]

      9. metadata-eval 94.3%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}} \]

      10. associate-*r* 94.2%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right)}} \]

      11. *-commutative 94.2%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}} \]

      12. *-commutative 94.2%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot -9\right)}\right)}} \]

   6. Simplified 94.2%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 68.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   8. Step-by-step derivation

      1. *-commutative 68.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-*l/ 68.9%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      3. associate-*r/ 68.8%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      4. associate-*l* 72.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      5. associate-*r/ 72.1%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   9. Simplified 72.1%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]

   if 1.35e26 < t

   1. Initial program 90.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.8%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 65.3%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. clear-num 65.3%

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{1}{\frac{a}{z}}}\right) \]

      2. un-div-inv 65.4%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Applied egg-rr 65.4%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-147}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.75e-147)
   (* -4.5 (/ (* t z) a))
   (if (<= t 1.35e+26) (* x (/ (* y 0.5) a)) (* -4.5 (/ t (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.75e-147) {
		tmp = -4.5 * ((t * z) / a);
	} else if (t <= 1.35e+26) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.75d-147)) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (t <= 1.35d+26) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.75e-147) {
		tmp = -4.5 * ((t * z) / a);
	} else if (t <= 1.35e+26) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.75e-147:
		tmp = -4.5 * ((t * z) / a)
	elif t <= 1.35e+26:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.75e-147)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (t <= 1.35e+26)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.75e-147)
		tmp = -4.5 * ((t * z) / a);
	elseif (t <= 1.35e+26)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.75e-147], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+26], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75000000000000002e-147

   1. Initial program 90.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 54.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if -1.75000000000000002e-147 < t < 1.35e26

   1. Initial program 94.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 68.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 71.1%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 71.1%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 72.1%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if 1.35e26 < t

   1. Initial program 90.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.8%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 65.3%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. clear-num 65.3%

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{1}{\frac{a}{z}}}\right) \]

      2. un-div-inv 65.4%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Applied egg-rr 65.4%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-147}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \frac{t \cdot z}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (/ (* t z) a)))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * ((t * z) / 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 = (-4.5d0) * ((t * z) / a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * ((t * z) / a);
}

Python

def code(x, y, z, t, a):
	return -4.5 * ((t * z) / a)

Julia

function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(Float64(t * z) / a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * ((t * z) / a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.9%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 50.6%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
4. Add Preprocessing

Alternative 17: 52.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \frac{t}{\frac{a}{z}} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (/ t (/ a z))))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t / (a / z));
}

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 = (-4.5d0) * (t / (a / z))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t / (a / z));
}

Python

def code(x, y, z, t, a):
	return -4.5 * (t / (a / z))

Julia

function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(t / Float64(a / z)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t / (a / z));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.9%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 50.6%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
4. Step-by-step derivation

   1. associate-/l* 50.6%

      \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

5. Simplified 50.6%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
6. Step-by-step derivation

   1. clear-num 50.6%

      \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{1}{\frac{a}{z}}}\right) \]

   2. un-div-inv 50.7%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

7. Applied egg-rr 50.7%

   \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]
8. Add Preprocessing

Alternative 18: 52.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (* t (/ z a))))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / 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 = (-4.5d0) * (t * (z / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Python

def code(x, y, z, t, a):
	return -4.5 * (t * (z / a))

Julia

function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(t * Float64(z / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t * (z / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.9%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 50.6%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
4. Step-by-step derivation

   1. associate-/l* 50.6%

      \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

5. Simplified 50.6%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
6. Add Preprocessing

Developer target: 93.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))