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

Percentage Accurate: 91.2% → 96.5%

Time: 29.5s

Alternatives: 13

Speedup: 0.4×

• 28.8% 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: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4.5, \frac{z}{a}, 0.5 \cdot \left(\frac{x}{a} \cdot \frac{y}{t}\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(t \cdot \frac{\mathsf{fma}\left(z, 9, x \cdot \frac{y}{-t}\right)}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* t (fma -4.5 (/ z a) (* 0.5 (* (/ x a) (/ y t)))))
     (if (<= t_1 5e+300)
       (/ (fma x (/ y 2.0) (* t (* z -4.5))) a)
       (* -0.5 (* t (/ (fma z 9.0 (* x (/ y (- t)))) a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t * fma(-4.5, (z / a), (0.5 * ((x / a) * (y / t))));
	} else if (t_1 <= 5e+300) {
		tmp = fma(x, (y / 2.0), (t * (z * -4.5))) / a;
	} else {
		tmp = -0.5 * (t * (fma(z, 9.0, (x * (y / -t))) / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t * fma(-4.5, Float64(z / a), Float64(0.5 * Float64(Float64(x / a) * Float64(y / t)))));
	elseif (t_1 <= 5e+300)
		tmp = Float64(fma(x, Float64(y / 2.0), Float64(t * Float64(z * -4.5))) / a);
	else
		tmp = Float64(-0.5 * Float64(t * Float64(fma(z, 9.0, Float64(x * Float64(y / Float64(-t)))) / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision] + N[(0.5 * N[(N[(x / a), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+300], N[(N[(x * N[(y / 2.0), $MachinePrecision] + N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(-0.5 * N[(t * N[(N[(z * 9.0 + N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0

   1. Initial program 72.0%

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

      1. cancel-sign-sub-inv 72.0%

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

      2. fma-define 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. associate-*r* 72.0%

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

      5. distribute-lft-neg-in 72.0%

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

      6. *-commutative 72.0%

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

      7. distribute-rgt-neg-in 72.0%

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

      8. metadata-eval 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in t around inf 86.9%

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

      1. fma-define 86.8%

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

      2. times-frac 99.9%

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

   7. Simplified 99.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.00000000000000026e300

   1. Initial program 98.6%

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

      1. associate-/l/ 99.0%

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

      2. div-sub 99.0%

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

      3. associate-/l* 99.0%

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

      4. fma-neg 99.0%

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

      5. *-commutative 99.0%

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

      6. associate-/l* 99.0%

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

      7. distribute-rgt-neg-out 99.0%

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

      8. distribute-frac-neg 99.0%

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

      9. distribute-rgt-neg-in 99.0%

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

      10. associate-/l* 99.0%

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

      11. metadata-eval 99.0%

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

      12. metadata-eval 99.0%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   if 5.00000000000000026e300 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 68.9%

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

      1. cancel-sign-sub-inv 68.9%

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

      2. fma-define 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. associate-*r* 74.4%

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

      5. distribute-lft-neg-in 74.4%

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

      6. *-commutative 74.4%

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

      7. distribute-rgt-neg-in 74.4%

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

      8. metadata-eval 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in t around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. metadata-eval 66.4%

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

      3. cancel-sign-sub-inv 66.4%

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

      4. *-commutative 66.4%

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

      5. distribute-rgt-neg-in 66.4%

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

      6. cancel-sign-sub-inv 66.4%

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

      7. metadata-eval 66.4%

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

      8. +-commutative 66.4%

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

      9. *-commutative 66.4%

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

      10. mul-1-neg 66.4%

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

      11. unsub-neg 66.4%

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

      12. *-commutative 66.4%

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

      13. associate-/l* 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in a around 0 66.4%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{t \cdot \left(9 \cdot z - \frac{x \cdot y}{t}\right)}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*r/ 91.7%

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

      4. fma-neg 91.7%

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

      5. distribute-rgt-neg-in 91.7%

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

      6. distribute-neg-frac 91.7%

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

   10. Simplified 91.7%

       \[\leadsto \color{blue}{-0.5 \cdot \left(t \cdot \frac{\mathsf{fma}\left(z, 9, x \cdot \frac{-y}{t}\right)}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4.5, \frac{z}{a}, 0.5 \cdot \left(\frac{x}{a} \cdot \frac{y}{t}\right)\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+300}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(t \cdot \frac{\mathsf{fma}\left(z, 9, x \cdot \frac{y}{-t}\right)}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+304}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(t \cdot \frac{\mathsf{fma}\left(z, 9, x \cdot \frac{y}{-t}\right)}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))))
   (if (<= t_1 -4e+304)
     (- (* 0.5 (* y (/ x a))) (* t (* (/ z a) 4.5)))
     (if (<= t_1 5e+292)
       (/ (fma x (/ y 2.0) (* t (* z -4.5))) a)
       (* -0.5 (* t (/ (fma z 9.0 (* x (/ y (- t)))) a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	double tmp;
	if (t_1 <= -4e+304) {
		tmp = (0.5 * (y * (x / a))) - (t * ((z / a) * 4.5));
	} else if (t_1 <= 5e+292) {
		tmp = fma(x, (y / 2.0), (t * (z * -4.5))) / a;
	} else {
		tmp = -0.5 * (t * (fma(z, 9.0, (x * (y / -t))) / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
	tmp = 0.0
	if (t_1 <= -4e+304)
		tmp = Float64(Float64(0.5 * Float64(y * Float64(x / a))) - Float64(t * Float64(Float64(z / a) * 4.5)));
	elseif (t_1 <= 5e+292)
		tmp = Float64(fma(x, Float64(y / 2.0), Float64(t * Float64(z * -4.5))) / a);
	else
		tmp = Float64(-0.5 * Float64(t * Float64(fma(z, 9.0, Float64(x * Float64(y / Float64(-t)))) / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+304], N[(N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+292], N[(N[(x * N[(y / 2.0), $MachinePrecision] + N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(-0.5 * N[(t * N[(N[(z * 9.0 + N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < -3.9999999999999998e304

   1. Initial program 91.8%

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

      1. cancel-sign-sub-inv 91.8%

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

      2. fma-define 91.8%

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

      3. distribute-rgt-neg-in 91.8%

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

      4. associate-*r* 91.8%

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

      5. distribute-lft-neg-in 91.8%

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

      6. *-commutative 91.8%

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

      7. distribute-rgt-neg-in 91.8%

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

      8. metadata-eval 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r* 91.8%

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

      3. metadata-eval 91.8%

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

      4. distribute-rgt-neg-in 91.8%

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

      5. distribute-lft-neg-in 91.8%

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

      6. fma-neg 91.8%

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

      7. div-sub 89.7%

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

      8. sub-neg 89.7%

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

      9. *-commutative 89.7%

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

      10. associate-/r* 89.7%

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

      11. associate-*r/ 89.7%

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

      12. div-inv 89.7%

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

      13. metadata-eval 89.7%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{0.5}\right)}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]

      14. associate-*l* 89.7%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\frac{\color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\right) \]

      15. associate-/l* 91.8%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\color{blue}{z \cdot \frac{9 \cdot t}{a \cdot 2}}\right) \]

   6. Applied egg-rr 91.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-z \cdot \frac{9 \cdot t}{a \cdot 2}\right)} \]
   7. Step-by-step derivation

      1. sub-neg 91.8%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} - z \cdot \frac{9 \cdot t}{a \cdot 2}} \]

      2. *-commutative 91.8%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\frac{9 \cdot t}{a \cdot 2} \cdot z} \]

      3. *-commutative 91.8%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \frac{9 \cdot t}{\color{blue}{2 \cdot a}} \cdot z \]

      4. times-frac 91.8%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\left(\frac{9}{2} \cdot \frac{t}{a}\right)} \cdot z \]

      5. metadata-eval 91.8%

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

      6. cancel-sign-sub-inv 91.8%

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

      7. distribute-lft-neg-in 91.8%

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

      8. distribute-rgt-neg-in 91.8%

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

      9. *-commutative 91.8%

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

      10. cancel-sign-sub-inv 91.8%

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

      11. associate-*r* 91.8%

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

      12. *-commutative 91.8%

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

      13. associate-*r/ 91.8%

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

      14. associate-/l* 97.9%

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

      15. *-commutative 97.9%

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

      16. associate-*r* 97.8%

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

      17. associate-/l* 95.8%

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

      18. *-commutative 95.8%

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

      19. associate-/l* 97.8%

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

      20. associate-*r* 97.8%

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

      21. *-commutative 97.8%

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

   8. Simplified 97.8%

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

      1. clear-num 97.8%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

      2. inv-pow 97.8%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   10. Applied egg-rr 97.8%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
   11. Step-by-step derivation

       1. unpow-1 97.8%

          \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   12. Simplified 97.8%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   13. Taylor expanded in x around 0 91.7%

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

       1. *-commutative 91.7%

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

       2. associate-/l* 91.4%

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

   15. Simplified 91.4%

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

   if -3.9999999999999998e304 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < 4.9999999999999996e292

   1. Initial program 98.3%

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

      1. associate-/l/ 98.9%

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

      2. div-sub 98.9%

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

      3. associate-/l* 98.9%

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

      4. fma-neg 98.9%

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

      5. *-commutative 98.9%

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

      6. associate-/l* 98.9%

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

      7. distribute-rgt-neg-out 98.9%

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

      8. distribute-frac-neg 98.9%

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

      9. distribute-rgt-neg-in 98.9%

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

      10. associate-/l* 98.9%

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

      11. metadata-eval 98.9%

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

      12. metadata-eval 98.9%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   if 4.9999999999999996e292 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64)))

   1. Initial program 67.8%

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

      1. cancel-sign-sub-inv 67.8%

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

      2. fma-define 69.9%

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

      3. distribute-rgt-neg-in 69.9%

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

      4. associate-*r* 71.8%

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

      5. distribute-lft-neg-in 71.8%

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

      6. *-commutative 71.8%

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

      7. distribute-rgt-neg-in 71.8%

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

      8. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in t around -inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. metadata-eval 68.0%

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

      3. cancel-sign-sub-inv 68.0%

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

      4. *-commutative 68.0%

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

      5. distribute-rgt-neg-in 68.0%

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

      6. cancel-sign-sub-inv 68.0%

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

      7. metadata-eval 68.0%

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

      8. +-commutative 68.0%

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

      9. *-commutative 68.0%

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

      10. mul-1-neg 68.0%

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

      11. unsub-neg 68.0%

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

      12. *-commutative 68.0%

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

      13. associate-/l* 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in a around 0 68.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{t \cdot \left(9 \cdot z - \frac{x \cdot y}{t}\right)}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r/ 92.2%

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

      4. fma-neg 92.2%

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

      5. distribute-rgt-neg-in 92.2%

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

      6. distribute-neg-frac 92.2%

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

   10. Simplified 92.2%

       \[\leadsto \color{blue}{-0.5 \cdot \left(t \cdot \frac{\mathsf{fma}\left(z, 9, x \cdot \frac{-y}{t}\right)}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \leq -4 \cdot 10^{+304}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{elif}\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(t \cdot \frac{\mathsf{fma}\left(z, 9, x \cdot \frac{y}{-t}\right)}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ t_2 := t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))) (t_2 (* t (* (/ z a) 4.5))))
   (if (<= t_1 (- INFINITY))
     (- (* 0.5 (* y (/ x a))) t_2)
     (if (<= t_1 2e+264)
       (/ (fma x (/ y 2.0) (* t (* z -4.5))) a)
       (- (* 0.5 (/ x (/ a y))) t_2)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double t_2 = t * ((z / a) * 4.5);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (0.5 * (y * (x / a))) - t_2;
	} else if (t_1 <= 2e+264) {
		tmp = fma(x, (y / 2.0), (t * (z * -4.5))) / a;
	} else {
		tmp = (0.5 * (x / (a / y))) - t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	t_2 = Float64(t * Float64(Float64(z / a) * 4.5))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(0.5 * Float64(y * Float64(x / a))) - t_2);
	elseif (t_1 <= 2e+264)
		tmp = Float64(fma(x, Float64(y / 2.0), Float64(t * Float64(z * -4.5))) / a);
	else
		tmp = Float64(Float64(0.5 * Float64(x / Float64(a / y))) - t_2);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 2e+264], N[(N[(x * N[(y / 2.0), $MachinePrecision] + N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0

   1. Initial program 72.0%

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

      1. cancel-sign-sub-inv 72.0%

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

      2. fma-define 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. associate-*r* 72.0%

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

      5. distribute-lft-neg-in 72.0%

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

      6. *-commutative 72.0%

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

      7. distribute-rgt-neg-in 72.0%

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

      8. metadata-eval 72.0%

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

   3. Simplified 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-*r* 72.0%

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

      3. metadata-eval 72.0%

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

      4. distribute-rgt-neg-in 72.0%

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

      5. distribute-lft-neg-in 72.0%

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

      6. fma-neg 72.0%

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

      7. div-sub 68.7%

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

      8. sub-neg 68.7%

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

      9. *-commutative 68.7%

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

      10. associate-/r* 68.7%

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

      11. associate-*r/ 68.7%

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

      12. div-inv 68.7%

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

      13. metadata-eval 68.7%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{0.5}\right)}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]

      14. associate-*l* 68.7%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\frac{\color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\right) \]

      15. associate-/l* 84.1%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\color{blue}{z \cdot \frac{9 \cdot t}{a \cdot 2}}\right) \]

   6. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-z \cdot \frac{9 \cdot t}{a \cdot 2}\right)} \]
   7. Step-by-step derivation

      1. sub-neg 84.1%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} - z \cdot \frac{9 \cdot t}{a \cdot 2}} \]

      2. *-commutative 84.1%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\frac{9 \cdot t}{a \cdot 2} \cdot z} \]

      3. *-commutative 84.1%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \frac{9 \cdot t}{\color{blue}{2 \cdot a}} \cdot z \]

      4. times-frac 84.2%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\left(\frac{9}{2} \cdot \frac{t}{a}\right)} \cdot z \]

      5. metadata-eval 84.2%

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

      6. cancel-sign-sub-inv 84.2%

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

      7. distribute-lft-neg-in 84.2%

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

      8. distribute-rgt-neg-in 84.2%

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

      9. *-commutative 84.2%

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

      10. cancel-sign-sub-inv 84.2%

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

      11. associate-*r* 84.2%

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

      12. *-commutative 84.2%

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

      13. associate-*r/ 84.2%

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

      14. associate-/l* 93.3%

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

      15. *-commutative 93.3%

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

      16. associate-*r* 93.2%

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

      17. associate-/l* 74.5%

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

      18. *-commutative 74.5%

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

      19. associate-/l* 93.1%

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

      20. associate-*r* 93.3%

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

      21. *-commutative 93.3%

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

   8. Simplified 93.3%

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

      1. clear-num 93.3%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

      2. inv-pow 93.3%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   10. Applied egg-rr 93.3%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
   11. Step-by-step derivation

       1. unpow-1 93.3%

          \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   12. Simplified 93.3%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   13. Taylor expanded in x around 0 84.3%

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

       1. *-commutative 84.3%

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

       2. associate-/l* 96.7%

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

   15. Simplified 96.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.00000000000000009e264

   1. Initial program 98.5%

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

      1. associate-/l/ 99.0%

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

      2. div-sub 99.0%

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

      3. associate-/l* 99.0%

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

      4. fma-neg 99.0%

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

      5. *-commutative 99.0%

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

      6. associate-/l* 99.0%

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

      7. distribute-rgt-neg-out 99.0%

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

      8. distribute-frac-neg 99.0%

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

      9. distribute-rgt-neg-in 99.0%

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

      10. associate-/l* 99.0%

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

      11. metadata-eval 99.0%

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

      12. metadata-eval 99.0%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   if 2.00000000000000009e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 71.4%

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

      1. cancel-sign-sub-inv 71.4%

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

      2. fma-define 74.1%

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

      3. distribute-rgt-neg-in 74.1%

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

      4. associate-*r* 76.5%

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

      5. distribute-lft-neg-in 76.5%

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

      6. *-commutative 76.5%

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

      7. distribute-rgt-neg-in 76.5%

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

      8. metadata-eval 76.5%

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

   3. Simplified 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r* 74.1%

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

      3. metadata-eval 74.1%

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

      4. distribute-rgt-neg-in 74.1%

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

      5. distribute-lft-neg-in 74.1%

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

      6. fma-neg 71.4%

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

      7. div-sub 68.7%

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

      8. sub-neg 68.7%

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

      9. *-commutative 68.7%

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

      10. associate-/r* 68.7%

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

      11. associate-*r/ 68.7%

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

      12. div-inv 68.7%

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

      13. metadata-eval 68.7%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{0.5}\right)}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]

      14. associate-*l* 71.1%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\frac{\color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\right) \]

      15. associate-/l* 86.7%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\color{blue}{z \cdot \frac{9 \cdot t}{a \cdot 2}}\right) \]

   6. Applied egg-rr 86.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-z \cdot \frac{9 \cdot t}{a \cdot 2}\right)} \]
   7. Step-by-step derivation

      1. sub-neg 86.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} - z \cdot \frac{9 \cdot t}{a \cdot 2}} \]

      2. *-commutative 86.7%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\frac{9 \cdot t}{a \cdot 2} \cdot z} \]

      3. *-commutative 86.7%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \frac{9 \cdot t}{\color{blue}{2 \cdot a}} \cdot z \]

      4. times-frac 86.8%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\left(\frac{9}{2} \cdot \frac{t}{a}\right)} \cdot z \]

      5. metadata-eval 86.8%

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

      6. cancel-sign-sub-inv 86.8%

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

      7. distribute-lft-neg-in 86.8%

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

      8. distribute-rgt-neg-in 86.8%

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

      9. *-commutative 86.8%

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

      10. cancel-sign-sub-inv 86.8%

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

      11. associate-*r* 86.8%

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

      12. *-commutative 86.8%

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

      13. associate-*r/ 86.8%

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

      14. associate-/l* 97.1%

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

      15. *-commutative 97.1%

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

      16. associate-*r* 97.0%

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

      17. associate-/l* 79.0%

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

      18. *-commutative 79.0%

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

      19. associate-/l* 94.7%

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

      20. associate-*r* 94.7%

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

      21. *-commutative 94.7%

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

   8. Simplified 94.7%

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

      1. clear-num 94.7%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

      2. inv-pow 94.7%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   10. Applied egg-rr 94.7%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
   11. Step-by-step derivation

       1. unpow-1 94.7%

          \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   12. Simplified 94.7%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
   13. Step-by-step derivation

       1. un-div-inv 94.7%

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

   14. Applied egg-rr 94.7%

       \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+248} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 -5e+248) (not (<= t_1 2e+264)))
     (- (* 0.5 (* x (/ y a))) (* t (* (/ z a) 4.5)))
     (/ t_1 (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -5e+248) || !(t_1 <= 2e+264)) {
		tmp = (0.5 * (x * (y / a))) - (t * ((z / a) * 4.5));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = (x * y) - ((z * 9.0d0) * t)
    if ((t_1 <= (-5d+248)) .or. (.not. (t_1 <= 2d+264))) then
        tmp = (0.5d0 * (x * (y / a))) - (t * ((z / a) * 4.5d0))
    else
        tmp = t_1 / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -5e+248) || !(t_1 <= 2e+264)) {
		tmp = (0.5 * (x * (y / a))) - (t * ((z / a) * 4.5));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -5e+248) or not (t_1 <= 2e+264):
		tmp = (0.5 * (x * (y / a))) - (t * ((z / a) * 4.5))
	else:
		tmp = t_1 / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= -5e+248) || !(t_1 <= 2e+264))
		tmp = Float64(Float64(0.5 * Float64(x * Float64(y / a))) - Float64(t * Float64(Float64(z / a) * 4.5)));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -5e+248) || ~((t_1 <= 2e+264)))
		tmp = (0.5 * (x * (y / a))) - (t * ((z / a) * 4.5));
	else
		tmp = t_1 / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+248], N[Not[LessEqual[t$95$1, 2e+264]], $MachinePrecision]], N[(N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -4.9999999999999996e248 or 2.00000000000000009e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 75.6%

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

      1. cancel-sign-sub-inv 75.6%

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

      2. fma-define 76.8%

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

      3. distribute-rgt-neg-in 76.8%

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

      4. associate-*r* 77.9%

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

      5. distribute-lft-neg-in 77.9%

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

      6. *-commutative 77.9%

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

      7. distribute-rgt-neg-in 77.9%

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

      8. metadata-eval 77.9%

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

   3. Simplified 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*r* 76.8%

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

      3. metadata-eval 76.8%

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

      4. distribute-rgt-neg-in 76.8%

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

      5. distribute-lft-neg-in 76.8%

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

      6. fma-neg 75.6%

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

      7. div-sub 73.1%

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

      8. sub-neg 73.1%

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

      9. *-commutative 73.1%

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

      10. associate-/r* 73.1%

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

      11. associate-*r/ 73.1%

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

      12. div-inv 73.1%

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

      13. metadata-eval 73.1%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{0.5}\right)}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]

      14. associate-*l* 74.2%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\frac{\color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\right) \]

      15. associate-/l* 87.0%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\color{blue}{z \cdot \frac{9 \cdot t}{a \cdot 2}}\right) \]

   6. Applied egg-rr 87.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-z \cdot \frac{9 \cdot t}{a \cdot 2}\right)} \]
   7. Step-by-step derivation

      1. sub-neg 87.0%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} - z \cdot \frac{9 \cdot t}{a \cdot 2}} \]

      2. *-commutative 87.0%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\frac{9 \cdot t}{a \cdot 2} \cdot z} \]

      3. *-commutative 87.0%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \frac{9 \cdot t}{\color{blue}{2 \cdot a}} \cdot z \]

      4. times-frac 88.1%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\left(\frac{9}{2} \cdot \frac{t}{a}\right)} \cdot z \]

      5. metadata-eval 88.1%

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

      6. cancel-sign-sub-inv 88.1%

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

      7. distribute-lft-neg-in 88.1%

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

      8. distribute-rgt-neg-in 88.1%

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

      9. *-commutative 88.1%

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

      10. cancel-sign-sub-inv 88.1%

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

      11. associate-*r* 88.1%

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

      12. *-commutative 88.1%

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

      13. associate-*r/ 88.1%

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

      14. associate-/l* 96.1%

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

      15. *-commutative 96.1%

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

      16. associate-*r* 96.1%

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

      17. associate-/l* 81.2%

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

      18. *-commutative 81.2%

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

      19. associate-/l* 93.8%

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

      20. associate-*r* 93.9%

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

      21. *-commutative 93.9%

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

   8. Simplified 93.9%

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

   if -4.9999999999999996e248 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.00000000000000009e264

   1. Initial program 99.0%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+248} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ t_2 := t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+248}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))) (t_2 (* t (* (/ z a) 4.5))))
   (if (<= t_1 -5e+248)
     (- (* 0.5 (* y (/ x a))) t_2)
     (if (<= t_1 2e+264) (/ t_1 (* a 2.0)) (- (* 0.5 (/ x (/ a y))) t_2)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double t_2 = t * ((z / a) * 4.5);
	double tmp;
	if (t_1 <= -5e+248) {
		tmp = (0.5 * (y * (x / a))) - t_2;
	} else if (t_1 <= 2e+264) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (0.5 * (x / (a / y))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    t_2 = t * ((z / a) * 4.5d0)
    if (t_1 <= (-5d+248)) then
        tmp = (0.5d0 * (y * (x / a))) - t_2
    else if (t_1 <= 2d+264) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = (0.5d0 * (x / (a / y))) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double t_2 = t * ((z / a) * 4.5);
	double tmp;
	if (t_1 <= -5e+248) {
		tmp = (0.5 * (y * (x / a))) - t_2;
	} else if (t_1 <= 2e+264) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (0.5 * (x / (a / y))) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	t_2 = t * ((z / a) * 4.5)
	tmp = 0
	if t_1 <= -5e+248:
		tmp = (0.5 * (y * (x / a))) - t_2
	elif t_1 <= 2e+264:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = (0.5 * (x / (a / y))) - t_2
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	t_2 = Float64(t * Float64(Float64(z / a) * 4.5))
	tmp = 0.0
	if (t_1 <= -5e+248)
		tmp = Float64(Float64(0.5 * Float64(y * Float64(x / a))) - t_2);
	elseif (t_1 <= 2e+264)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(Float64(0.5 * Float64(x / Float64(a / y))) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	t_2 = t * ((z / a) * 4.5);
	tmp = 0.0;
	if (t_1 <= -5e+248)
		tmp = (0.5 * (y * (x / a))) - t_2;
	elseif (t_1 <= 2e+264)
		tmp = t_1 / (a * 2.0);
	else
		tmp = (0.5 * (x / (a / y))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+248], N[(N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 2e+264], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -4.9999999999999996e248

   1. Initial program 79.0%

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

      1. cancel-sign-sub-inv 79.0%

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

      2. fma-define 79.0%

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

      3. distribute-rgt-neg-in 79.0%

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

      4. associate-*r* 79.0%

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

      5. distribute-lft-neg-in 79.0%

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

      6. *-commutative 79.0%

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

      7. distribute-rgt-neg-in 79.0%

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

      8. metadata-eval 79.0%

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

   3. Simplified 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-*r* 79.0%

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

      3. metadata-eval 79.0%

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

      4. distribute-rgt-neg-in 79.0%

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

      5. distribute-lft-neg-in 79.0%

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

      6. fma-neg 79.0%

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

      7. div-sub 76.8%

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

      8. sub-neg 76.8%

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

      9. *-commutative 76.8%

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

      10. associate-/r* 76.8%

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

      11. associate-*r/ 76.8%

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

      12. div-inv 76.8%

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

      13. metadata-eval 76.8%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{0.5}\right)}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]

      14. associate-*l* 76.8%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\frac{\color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\right) \]

      15. associate-/l* 87.1%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\color{blue}{z \cdot \frac{9 \cdot t}{a \cdot 2}}\right) \]

   6. Applied egg-rr 87.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-z \cdot \frac{9 \cdot t}{a \cdot 2}\right)} \]
   7. Step-by-step derivation

      1. sub-neg 87.1%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} - z \cdot \frac{9 \cdot t}{a \cdot 2}} \]

      2. *-commutative 87.1%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\frac{9 \cdot t}{a \cdot 2} \cdot z} \]

      3. *-commutative 87.1%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \frac{9 \cdot t}{\color{blue}{2 \cdot a}} \cdot z \]

      4. times-frac 89.3%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\left(\frac{9}{2} \cdot \frac{t}{a}\right)} \cdot z \]

      5. metadata-eval 89.3%

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

      6. cancel-sign-sub-inv 89.3%

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

      7. distribute-lft-neg-in 89.3%

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

      8. distribute-rgt-neg-in 89.3%

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

      9. *-commutative 89.3%

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

      10. cancel-sign-sub-inv 89.3%

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

      11. associate-*r* 89.3%

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

      12. *-commutative 89.3%

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

      13. associate-*r/ 89.3%

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

      14. associate-/l* 95.3%

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

      15. *-commutative 95.3%

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

      16. associate-*r* 95.4%

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

      17. associate-/l* 82.9%

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

      18. *-commutative 82.9%

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

      19. associate-/l* 93.1%

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

      20. associate-*r* 93.2%

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

      21. *-commutative 93.2%

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

   8. Simplified 93.2%

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

      1. clear-num 93.2%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

      2. inv-pow 93.2%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   10. Applied egg-rr 93.2%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
   11. Step-by-step derivation

       1. unpow-1 93.2%

          \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   12. Simplified 93.2%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   13. Taylor expanded in x around 0 87.2%

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

       1. *-commutative 87.2%

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

       2. associate-/l* 95.5%

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

   15. Simplified 95.5%

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

   if -4.9999999999999996e248 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.00000000000000009e264

   1. Initial program 99.0%

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

   if 2.00000000000000009e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 71.4%

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

      1. cancel-sign-sub-inv 71.4%

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

      2. fma-define 74.1%

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

      3. distribute-rgt-neg-in 74.1%

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

      4. associate-*r* 76.5%

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

      5. distribute-lft-neg-in 76.5%

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

      6. *-commutative 76.5%

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

      7. distribute-rgt-neg-in 76.5%

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

      8. metadata-eval 76.5%

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

   3. Simplified 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r* 74.1%

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

      3. metadata-eval 74.1%

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

      4. distribute-rgt-neg-in 74.1%

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

      5. distribute-lft-neg-in 74.1%

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

      6. fma-neg 71.4%

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

      7. div-sub 68.7%

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

      8. sub-neg 68.7%

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

      9. *-commutative 68.7%

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

      10. associate-/r* 68.7%

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

      11. associate-*r/ 68.7%

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

      12. div-inv 68.7%

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

      13. metadata-eval 68.7%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{0.5}\right)}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]

      14. associate-*l* 71.1%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\frac{\color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\right) \]

      15. associate-/l* 86.7%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\color{blue}{z \cdot \frac{9 \cdot t}{a \cdot 2}}\right) \]

   6. Applied egg-rr 86.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-z \cdot \frac{9 \cdot t}{a \cdot 2}\right)} \]
   7. Step-by-step derivation

      1. sub-neg 86.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} - z \cdot \frac{9 \cdot t}{a \cdot 2}} \]

      2. *-commutative 86.7%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\frac{9 \cdot t}{a \cdot 2} \cdot z} \]

      3. *-commutative 86.7%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \frac{9 \cdot t}{\color{blue}{2 \cdot a}} \cdot z \]

      4. times-frac 86.8%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\left(\frac{9}{2} \cdot \frac{t}{a}\right)} \cdot z \]

      5. metadata-eval 86.8%

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

      6. cancel-sign-sub-inv 86.8%

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

      7. distribute-lft-neg-in 86.8%

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

      8. distribute-rgt-neg-in 86.8%

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

      9. *-commutative 86.8%

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

      10. cancel-sign-sub-inv 86.8%

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

      11. associate-*r* 86.8%

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

      12. *-commutative 86.8%

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

      13. associate-*r/ 86.8%

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

      14. associate-/l* 97.1%

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

      15. *-commutative 97.1%

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

      16. associate-*r* 97.0%

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

      17. associate-/l* 79.0%

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

      18. *-commutative 79.0%

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

      19. associate-/l* 94.7%

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

      20. associate-*r* 94.7%

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

      21. *-commutative 94.7%

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

   8. Simplified 94.7%

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

      1. clear-num 94.7%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

      2. inv-pow 94.7%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   10. Applied egg-rr 94.7%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
   11. Step-by-step derivation

       1. unpow-1 94.7%

          \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   12. Simplified 94.7%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
   13. Step-by-step derivation

       1. un-div-inv 94.7%

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

   14. Applied egg-rr 94.7%

       \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+248}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ t_2 := t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+248}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))) (t_2 (* t (* (/ z a) 4.5))))
   (if (<= t_1 -5e+248)
     (- (* 0.5 (* y (/ x a))) t_2)
     (if (<= t_1 2e+264) (/ t_1 (* a 2.0)) (- (* 0.5 (* x (/ y a))) t_2)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double t_2 = t * ((z / a) * 4.5);
	double tmp;
	if (t_1 <= -5e+248) {
		tmp = (0.5 * (y * (x / a))) - t_2;
	} else if (t_1 <= 2e+264) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (0.5 * (x * (y / a))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    t_2 = t * ((z / a) * 4.5d0)
    if (t_1 <= (-5d+248)) then
        tmp = (0.5d0 * (y * (x / a))) - t_2
    else if (t_1 <= 2d+264) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = (0.5d0 * (x * (y / a))) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double t_2 = t * ((z / a) * 4.5);
	double tmp;
	if (t_1 <= -5e+248) {
		tmp = (0.5 * (y * (x / a))) - t_2;
	} else if (t_1 <= 2e+264) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (0.5 * (x * (y / a))) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	t_2 = t * ((z / a) * 4.5)
	tmp = 0
	if t_1 <= -5e+248:
		tmp = (0.5 * (y * (x / a))) - t_2
	elif t_1 <= 2e+264:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = (0.5 * (x * (y / a))) - t_2
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	t_2 = Float64(t * Float64(Float64(z / a) * 4.5))
	tmp = 0.0
	if (t_1 <= -5e+248)
		tmp = Float64(Float64(0.5 * Float64(y * Float64(x / a))) - t_2);
	elseif (t_1 <= 2e+264)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(Float64(0.5 * Float64(x * Float64(y / a))) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	t_2 = t * ((z / a) * 4.5);
	tmp = 0.0;
	if (t_1 <= -5e+248)
		tmp = (0.5 * (y * (x / a))) - t_2;
	elseif (t_1 <= 2e+264)
		tmp = t_1 / (a * 2.0);
	else
		tmp = (0.5 * (x * (y / a))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+248], N[(N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 2e+264], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -4.9999999999999996e248

   1. Initial program 79.0%

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

      1. cancel-sign-sub-inv 79.0%

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

      2. fma-define 79.0%

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

      3. distribute-rgt-neg-in 79.0%

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

      4. associate-*r* 79.0%

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

      5. distribute-lft-neg-in 79.0%

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

      6. *-commutative 79.0%

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

      7. distribute-rgt-neg-in 79.0%

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

      8. metadata-eval 79.0%

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

   3. Simplified 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-*r* 79.0%

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

      3. metadata-eval 79.0%

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

      4. distribute-rgt-neg-in 79.0%

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

      5. distribute-lft-neg-in 79.0%

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

      6. fma-neg 79.0%

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

      7. div-sub 76.8%

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

      8. sub-neg 76.8%

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

      9. *-commutative 76.8%

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

      10. associate-/r* 76.8%

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

      11. associate-*r/ 76.8%

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

      12. div-inv 76.8%

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

      13. metadata-eval 76.8%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{0.5}\right)}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]

      14. associate-*l* 76.8%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\frac{\color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\right) \]

      15. associate-/l* 87.1%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\color{blue}{z \cdot \frac{9 \cdot t}{a \cdot 2}}\right) \]

   6. Applied egg-rr 87.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-z \cdot \frac{9 \cdot t}{a \cdot 2}\right)} \]
   7. Step-by-step derivation

      1. sub-neg 87.1%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} - z \cdot \frac{9 \cdot t}{a \cdot 2}} \]

      2. *-commutative 87.1%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\frac{9 \cdot t}{a \cdot 2} \cdot z} \]

      3. *-commutative 87.1%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \frac{9 \cdot t}{\color{blue}{2 \cdot a}} \cdot z \]

      4. times-frac 89.3%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\left(\frac{9}{2} \cdot \frac{t}{a}\right)} \cdot z \]

      5. metadata-eval 89.3%

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

      6. cancel-sign-sub-inv 89.3%

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

      7. distribute-lft-neg-in 89.3%

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

      8. distribute-rgt-neg-in 89.3%

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

      9. *-commutative 89.3%

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

      10. cancel-sign-sub-inv 89.3%

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

      11. associate-*r* 89.3%

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

      12. *-commutative 89.3%

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

      13. associate-*r/ 89.3%

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

      14. associate-/l* 95.3%

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

      15. *-commutative 95.3%

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

      16. associate-*r* 95.4%

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

      17. associate-/l* 82.9%

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

      18. *-commutative 82.9%

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

      19. associate-/l* 93.1%

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

      20. associate-*r* 93.2%

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

      21. *-commutative 93.2%

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

   8. Simplified 93.2%

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

      1. clear-num 93.2%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

      2. inv-pow 93.2%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   10. Applied egg-rr 93.2%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{{\left(\frac{a}{y}\right)}^{-1}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]
   11. Step-by-step derivation

       1. unpow-1 93.2%

          \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   12. Simplified 93.2%

       \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right) \]

   13. Taylor expanded in x around 0 87.2%

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

       1. *-commutative 87.2%

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

       2. associate-/l* 95.5%

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

   15. Simplified 95.5%

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

   if -4.9999999999999996e248 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.00000000000000009e264

   1. Initial program 99.0%

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

   if 2.00000000000000009e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 71.4%

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

      1. cancel-sign-sub-inv 71.4%

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

      2. fma-define 74.1%

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

      3. distribute-rgt-neg-in 74.1%

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

      4. associate-*r* 76.5%

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

      5. distribute-lft-neg-in 76.5%

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

      6. *-commutative 76.5%

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

      7. distribute-rgt-neg-in 76.5%

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

      8. metadata-eval 76.5%

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

   3. Simplified 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r* 74.1%

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

      3. metadata-eval 74.1%

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

      4. distribute-rgt-neg-in 74.1%

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

      5. distribute-lft-neg-in 74.1%

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

      6. fma-neg 71.4%

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

      7. div-sub 68.7%

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

      8. sub-neg 68.7%

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

      9. *-commutative 68.7%

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

      10. associate-/r* 68.7%

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

      11. associate-*r/ 68.7%

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

      12. div-inv 68.7%

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

      13. metadata-eval 68.7%

          \[\leadsto \frac{x \cdot \left(y \cdot \color{blue}{0.5}\right)}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]

      14. associate-*l* 71.1%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\frac{\color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2}\right) \]

      15. associate-/l* 86.7%

          \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-\color{blue}{z \cdot \frac{9 \cdot t}{a \cdot 2}}\right) \]

   6. Applied egg-rr 86.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} + \left(-z \cdot \frac{9 \cdot t}{a \cdot 2}\right)} \]
   7. Step-by-step derivation

      1. sub-neg 86.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot 0.5\right)}{a} - z \cdot \frac{9 \cdot t}{a \cdot 2}} \]

      2. *-commutative 86.7%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\frac{9 \cdot t}{a \cdot 2} \cdot z} \]

      3. *-commutative 86.7%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \frac{9 \cdot t}{\color{blue}{2 \cdot a}} \cdot z \]

      4. times-frac 86.8%

         \[\leadsto \frac{x \cdot \left(y \cdot 0.5\right)}{a} - \color{blue}{\left(\frac{9}{2} \cdot \frac{t}{a}\right)} \cdot z \]

      5. metadata-eval 86.8%

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

      6. cancel-sign-sub-inv 86.8%

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

      7. distribute-lft-neg-in 86.8%

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

      8. distribute-rgt-neg-in 86.8%

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

      9. *-commutative 86.8%

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

      10. cancel-sign-sub-inv 86.8%

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

      11. associate-*r* 86.8%

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

      12. *-commutative 86.8%

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

      13. associate-*r/ 86.8%

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

      14. associate-/l* 97.1%

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

      15. *-commutative 97.1%

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

      16. associate-*r* 97.0%

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

      17. associate-/l* 79.0%

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

      18. *-commutative 79.0%

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

      19. associate-/l* 94.7%

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

      20. associate-*r* 94.7%

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

      21. *-commutative 94.7%

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

   8. Simplified 94.7%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right) - t \cdot \left(4.5 \cdot \frac{z}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+248}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+200}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z \cdot -4.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* (/ z a) (* t -4.5))
     (if (<= t_1 5e+200)
       (/ (- (* x y) t_1) (* a 2.0))
       (* t (/ (* z -4.5) a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (z / a) * (t * -4.5);
	} else if (t_1 <= 5e+200) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = t * ((z * -4.5) / a);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (z / a) * (t * -4.5);
	} else if (t_1 <= 5e+200) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = t * ((z * -4.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (z / a) * (t * -4.5)
	elif t_1 <= 5e+200:
		tmp = ((x * y) - t_1) / (a * 2.0)
	else:
		tmp = t * ((z * -4.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	elseif (t_1 <= 5e+200)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	else
		tmp = Float64(t * Float64(Float64(z * -4.5) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (z / a) * (t * -4.5);
	elseif (t_1 <= 5e+200)
		tmp = ((x * y) - t_1) / (a * 2.0);
	else
		tmp = t * ((z * -4.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+200], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0

   1. Initial program 62.6%

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

      1. cancel-sign-sub-inv 62.6%

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

      2. fma-define 66.9%

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

      3. distribute-rgt-neg-in 66.9%

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

      4. associate-*r* 70.8%

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

      5. distribute-lft-neg-in 70.8%

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

      6. *-commutative 70.8%

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

      7. distribute-rgt-neg-in 70.8%

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

      8. metadata-eval 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in x around 0 75.0%

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

      1. associate-/l* 91.6%

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

      2. *-commutative 91.6%

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

      3. associate-*l* 91.6%

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

      4. *-commutative 91.6%

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

      5. associate-*l* 91.7%

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

      6. *-commutative 91.7%

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

   7. Simplified 91.7%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 5.00000000000000019e200

   1. Initial program 97.8%

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

   if 5.00000000000000019e200 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 73.0%

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

      1. cancel-sign-sub-inv 73.0%

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

      2. fma-define 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

      4. associate-*r* 73.0%

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

      5. distribute-lft-neg-in 73.0%

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

      6. *-commutative 73.0%

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

      7. distribute-rgt-neg-in 73.0%

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

      8. metadata-eval 73.0%

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

   3. Simplified 73.0%

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

      1. clear-num 73.1%

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

      2. inv-pow 73.1%

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

   6. Applied egg-rr 73.1%

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

      1. unpow-1 73.1%

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

      2. associate-/l* 76.0%

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

      3. fma-define 76.0%

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

      4. +-commutative 76.0%

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

      5. fma-define 76.1%

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

   8. Simplified 76.1%

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

   9. Taylor expanded in z around inf 76.1%

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

       1. metadata-eval 76.1%

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

       2. associate-*r/ 87.5%

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

       3. distribute-lft-neg-in 87.5%

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

       4. *-commutative 87.5%

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

       5. *-commutative 87.5%

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

       6. associate-*r* 87.5%

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

       7. *-commutative 87.5%

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

       8. associate-*l* 87.6%

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

       9. *-commutative 87.6%

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

       10. distribute-rgt-neg-in 87.6%

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

       11. *-commutative 87.6%

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

       12. associate-*r/ 87.6%

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

       13. distribute-frac-neg 87.6%

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

       14. *-commutative 87.6%

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

       15. distribute-rgt-neg-in 87.6%

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

       16. metadata-eval 87.6%

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

   11. Simplified 87.6%

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

Alternative 8: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+18)
   (* (/ x a) (* y 0.5))
   (if (<= (* x y) 1e-15) (/ (* -4.5 (* z t)) a) (/ (* y (* x 0.5)) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+18) {
		tmp = (x / a) * (y * 0.5);
	} else if ((x * y) <= 1e-15) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = (y * (x * 0.5)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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+18)) then
        tmp = (x / a) * (y * 0.5d0)
    else if ((x * y) <= 1d-15) then
        tmp = ((-4.5d0) * (z * t)) / a
    else
        tmp = (y * (x * 0.5d0)) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+18) {
		tmp = (x / a) * (y * 0.5);
	} else if ((x * y) <= 1e-15) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = (y * (x * 0.5)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+18:
		tmp = (x / a) * (y * 0.5)
	elif (x * y) <= 1e-15:
		tmp = (-4.5 * (z * t)) / a
	else:
		tmp = (y * (x * 0.5)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+18)
		tmp = Float64(Float64(x / a) * Float64(y * 0.5));
	elseif (Float64(x * y) <= 1e-15)
		tmp = Float64(Float64(-4.5 * Float64(z * t)) / a);
	else
		tmp = Float64(Float64(y * Float64(x * 0.5)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+18)
		tmp = (x / a) * (y * 0.5);
	elseif ((x * y) <= 1e-15)
		tmp = (-4.5 * (z * t)) / a;
	else
		tmp = (y * (x * 0.5)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+18], N[(N[(x / a), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-15], N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e18

   1. Initial program 86.0%

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

      1. associate-/l/ 86.0%

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

      2. div-sub 86.0%

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

      3. associate-/l* 86.0%

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

      4. fma-neg 87.6%

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

      5. *-commutative 87.6%

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

      6. associate-/l* 87.6%

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

      7. distribute-rgt-neg-out 87.6%

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

      8. distribute-frac-neg 87.6%

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

      9. distribute-rgt-neg-in 87.6%

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

      10. associate-/l* 87.6%

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

      11. metadata-eval 87.6%

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

      12. metadata-eval 87.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.5%

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

      1. associate-*r* 70.5%

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

      2. *-commutative 70.5%

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

   7. Simplified 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-*l* 70.5%

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

      3. associate-*r/ 70.5%

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

      4. *-commutative 70.5%

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

      5. associate-*r/ 69.4%

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

      6. *-commutative 69.4%

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

      7. *-commutative 69.4%

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

      8. associate-*l* 69.4%

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

   9. Applied egg-rr 69.4%

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

   if -2e18 < (*.f64 x y) < 1.0000000000000001e-15

   1. Initial program 93.3%

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

      1. associate-/l/ 94.0%

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

      2. div-sub 94.0%

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

      3. associate-/l* 94.0%

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

      4. fma-neg 94.0%

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

      5. *-commutative 94.0%

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

      6. associate-/l* 94.0%

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

      7. distribute-rgt-neg-out 94.0%

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

      8. distribute-frac-neg 94.0%

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

      9. distribute-rgt-neg-in 94.0%

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

      10. associate-/l* 94.7%

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

      11. metadata-eval 94.7%

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

      12. metadata-eval 94.7%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.5%

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

   if 1.0000000000000001e-15 < (*.f64 x y)

   1. Initial program 93.1%

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

      1. associate-/l/ 93.1%

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

      2. div-sub 93.1%

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

      3. associate-/l* 93.1%

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

      4. fma-neg 93.1%

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

      5. *-commutative 93.1%

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

      6. associate-/l* 93.1%

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

      7. distribute-rgt-neg-out 93.1%

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

      8. distribute-frac-neg 93.1%

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

      9. distribute-rgt-neg-in 93.1%

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

      10. associate-/l* 93.1%

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

      11. metadata-eval 93.1%

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

      12. metadata-eval 93.1%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 74.6%

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

      1. associate-*r* 74.6%

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

      2. *-commutative 74.6%

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

   7. Simplified 74.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-15}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+106} \lor \neg \left(x \leq 1.25 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.5e+106) (not (<= x 1.25e-90)))
   (* (/ x a) (* y 0.5))
   (/ (* -4.5 (* z t)) a)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.5e+106) || !(x <= 1.25e-90)) {
		tmp = (x / a) * (y * 0.5);
	} else {
		tmp = (-4.5 * (z * t)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= (-4.5d+106)) .or. (.not. (x <= 1.25d-90))) then
        tmp = (x / a) * (y * 0.5d0)
    else
        tmp = ((-4.5d0) * (z * t)) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.5e+106) || !(x <= 1.25e-90)) {
		tmp = (x / a) * (y * 0.5);
	} else {
		tmp = (-4.5 * (z * t)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.5e+106) or not (x <= 1.25e-90):
		tmp = (x / a) * (y * 0.5)
	else:
		tmp = (-4.5 * (z * t)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.5e+106) || !(x <= 1.25e-90))
		tmp = Float64(Float64(x / a) * Float64(y * 0.5));
	else
		tmp = Float64(Float64(-4.5 * Float64(z * t)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.5e+106) || ~((x <= 1.25e-90)))
		tmp = (x / a) * (y * 0.5);
	else
		tmp = (-4.5 * (z * t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.5e+106], N[Not[LessEqual[x, 1.25e-90]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4999999999999997e106 or 1.25000000000000005e-90 < x

   1. Initial program 88.5%

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

      1. associate-/l/ 88.5%

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

      2. div-sub 88.5%

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

      3. associate-/l* 88.5%

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

      4. fma-neg 89.3%

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

      5. *-commutative 89.3%

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

      6. associate-/l* 89.3%

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

      7. distribute-rgt-neg-out 89.3%

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

      8. distribute-frac-neg 89.3%

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

      9. distribute-rgt-neg-in 89.3%

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

      10. associate-/l* 90.0%

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

      11. metadata-eval 90.0%

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

      12. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.7%

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

      1. associate-*r* 59.7%

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

      2. *-commutative 59.7%

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

   7. Simplified 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-*l* 59.7%

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

      3. associate-*r/ 59.7%

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

      4. *-commutative 59.7%

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

      5. associate-*r/ 61.9%

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

      6. *-commutative 61.9%

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

      7. *-commutative 61.9%

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

      8. associate-*l* 61.9%

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

   9. Applied egg-rr 61.9%

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

   if -4.4999999999999997e106 < x < 1.25000000000000005e-90

   1. Initial program 94.5%

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

      1. associate-/l/ 95.2%

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

      2. div-sub 95.2%

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

      3. associate-/l* 95.2%

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

      4. fma-neg 95.2%

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

      5. *-commutative 95.2%

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

      6. associate-/l* 95.2%

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

      7. distribute-rgt-neg-out 95.2%

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

      8. distribute-frac-neg 95.2%

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

      9. distribute-rgt-neg-in 95.2%

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

      10. associate-/l* 95.2%

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

      11. metadata-eval 95.2%

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

      12. metadata-eval 95.2%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.7%

      \[\leadsto \frac{\color{blue}{-4.5 \cdot \left(t \cdot z\right)}}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+106} \lor \neg \left(x \leq 1.25 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+107} \lor \neg \left(x \leq 9 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.45e+107) (not (<= x 9e-91)))
   (* (/ x a) (* y 0.5))
   (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e+107) || !(x <= 9e-91)) {
		tmp = (x / a) * (y * 0.5);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= (-1.45d+107)) .or. (.not. (x <= 9d-91))) then
        tmp = (x / a) * (y * 0.5d0)
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e+107) || !(x <= 9e-91)) {
		tmp = (x / a) * (y * 0.5);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.45e+107) or not (x <= 9e-91):
		tmp = (x / a) * (y * 0.5)
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.45e+107) || !(x <= 9e-91))
		tmp = Float64(Float64(x / a) * Float64(y * 0.5));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.45e+107) || ~((x <= 9e-91)))
		tmp = (x / a) * (y * 0.5);
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.45e+107], N[Not[LessEqual[x, 9e-91]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999994e107 or 8.99999999999999952e-91 < x

   1. Initial program 88.5%

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

      1. associate-/l/ 88.5%

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

      2. div-sub 88.5%

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

      3. associate-/l* 88.5%

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

      4. fma-neg 89.3%

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

      5. *-commutative 89.3%

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

      6. associate-/l* 89.3%

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

      7. distribute-rgt-neg-out 89.3%

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

      8. distribute-frac-neg 89.3%

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

      9. distribute-rgt-neg-in 89.3%

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

      10. associate-/l* 90.0%

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

      11. metadata-eval 90.0%

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

      12. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.7%

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

      1. associate-*r* 59.7%

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

      2. *-commutative 59.7%

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

   7. Simplified 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-*l* 59.7%

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

      3. associate-*r/ 59.7%

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

      4. *-commutative 59.7%

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

      5. associate-*r/ 61.9%

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

      6. *-commutative 61.9%

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

      7. *-commutative 61.9%

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

      8. associate-*l* 61.9%

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

   9. Applied egg-rr 61.9%

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

   if -1.44999999999999994e107 < x < 8.99999999999999952e-91

   1. Initial program 94.5%

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

      1. cancel-sign-sub-inv 94.5%

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

      2. fma-define 94.5%

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

      3. distribute-rgt-neg-in 94.5%

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

      4. associate-*r* 94.4%

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

      5. distribute-lft-neg-in 94.4%

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

      6. *-commutative 94.4%

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

      7. distribute-rgt-neg-in 94.4%

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

      8. metadata-eval 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+107} \lor \neg \left(x \leq 9 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+138} \lor \neg \left(x \leq 1.25 \cdot 10^{-90}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.8e+138) (not (<= x 1.25e-90)))
   (* 0.5 (* x (/ y a)))
   (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.8e+138) || !(x <= 1.25e-90)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= (-2.8d+138)) .or. (.not. (x <= 1.25d-90))) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.8e+138) || !(x <= 1.25e-90)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.8e+138) or not (x <= 1.25e-90):
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.8e+138) || !(x <= 1.25e-90))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.8e+138) || ~((x <= 1.25e-90)))
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.8e+138], N[Not[LessEqual[x, 1.25e-90]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e138 or 1.25000000000000005e-90 < x

   1. Initial program 87.7%

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

      1. cancel-sign-sub-inv 87.7%

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

      2. fma-define 88.6%

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

      3. distribute-rgt-neg-in 88.6%

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

      4. associate-*r* 89.4%

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

      5. distribute-lft-neg-in 89.4%

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

      6. *-commutative 89.4%

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

      7. distribute-rgt-neg-in 89.4%

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

      8. metadata-eval 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf 59.4%

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

      1. associate-/l* 59.3%

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

   7. Simplified 59.3%

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

   if -2.8000000000000001e138 < x < 1.25000000000000005e-90

   1. Initial program 94.8%

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

      1. cancel-sign-sub-inv 94.8%

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

      2. fma-define 94.8%

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

      3. distribute-rgt-neg-in 94.8%

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

      4. associate-*r* 94.8%

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

      5. distribute-lft-neg-in 94.8%

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

      6. *-commutative 94.8%

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

      7. distribute-rgt-neg-in 94.8%

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

      8. metadata-eval 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in x around 0 74.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+138} \lor \neg \left(x \leq 1.25 \cdot 10^{-90}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.7 \cdot 10^{+244}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 1.7e+244) (* -4.5 (/ (* z t) a)) (* -4.5 (* t (/ z a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.7e+244) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= 1.7d+244) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.7e+244) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 1.7e+244:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 1.7e+244)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 1.7e+244)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 1.7e+244], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.70000000000000005e244

   1. Initial program 93.2%

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

      1. cancel-sign-sub-inv 93.2%

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

      2. fma-define 93.6%

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

      3. distribute-rgt-neg-in 93.6%

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

      4. associate-*r* 94.0%

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

      5. distribute-lft-neg-in 94.0%

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

      6. *-commutative 94.0%

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

      7. distribute-rgt-neg-in 94.0%

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

      8. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around 0 57.6%

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

   if 1.70000000000000005e244 < a

   1. Initial program 72.3%

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

      1. cancel-sign-sub-inv 72.3%

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

      2. fma-define 72.3%

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

      3. distribute-rgt-neg-in 72.3%

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

      4. associate-*r* 72.3%

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

      5. distribute-lft-neg-in 72.3%

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

      6. *-commutative 72.3%

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

      7. distribute-rgt-neg-in 72.3%

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

      8. metadata-eval 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in x around 0 50.0%

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

      1. associate-/l* 45.7%

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

   7. Simplified 45.7%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.7 \cdot 10^{+244}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (* t (/ z a))))

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

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

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t * (z / a));
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.5%

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

   1. cancel-sign-sub-inv 91.5%

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

   2. fma-define 91.9%

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

   3. distribute-rgt-neg-in 91.9%

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

   4. associate-*r* 92.2%

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

   5. distribute-lft-neg-in 92.2%

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

   6. *-commutative 92.2%

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

   7. distribute-rgt-neg-in 92.2%

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

   8. metadata-eval 92.2%

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

3. Simplified 92.2%

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

5. Taylor expanded in x around 0 57.0%

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

   1. associate-/l* 54.9%

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

7. Simplified 54.9%

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

Developer Target 1: 93.8% 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 2024143 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -209046455797670900000000000000000000000000000000000000000000000000000000000000000000000) (- (* 1/2 (/ (* y x) a)) (* 9/2 (/ t (/ a z)))) (if (< a 2144030707833976000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 1/2)) (* (/ t a) (* z 9/2))))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))