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

Percentage Accurate: 91.1% → 97.0%

Time: 8.2s

Alternatives: 9

Speedup: 0.8×

• 27.8% 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: 91.1% 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: 97.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right) + -4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (fma -4.5 (/ t (/ a z)) (* 0.5 (/ x (/ a y))))
     (if (<= t_1 5e+284)
       (/ t_1 (* a 2.0))
       (+ (* x (* 0.5 (/ y 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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(-4.5, (t / (a / z)), (0.5 * (x / (a / y))));
	} else if (t_1 <= 5e+284) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (x * (0.5 * (y / a))) + (-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)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(-4.5, Float64(t / Float64(a / z)), Float64(0.5 * Float64(x / Float64(a / y))));
	elseif (t_1 <= 5e+284)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(Float64(x * Float64(0.5 * Float64(y / a))) + Float64(-4.5 * Float64(t * Float64(z / 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[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+284], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   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. associate-*l* 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in x around 0 68.4%

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

      1. fma-def 68.4%

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

      2. associate-/l* 85.5%

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

      3. associate-/l* 96.9%

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

   6. Simplified 96.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.9999999999999999e284

   1. Initial program 98.2%

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

   if 4.9999999999999999e284 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 67.2%

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

      1. associate-*l* 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in x around 0 67.2%

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

      1. fma-def 67.2%

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

      2. associate-/l* 76.9%

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

      3. associate-/l* 96.4%

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

   6. Simplified 96.4%

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

      1. fma-udef 96.4%

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

      2. associate-*r/ 96.5%

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

      3. +-commutative 96.5%

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

      4. *-commutative 96.5%

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

      5. div-inv 96.4%

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

      6. clear-num 96.4%

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

      7. associate-*l* 96.4%

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

      8. div-inv 96.4%

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

      9. clear-num 96.4%

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

      10. associate-*r* 96.4%

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

   8. Applied egg-rr 96.4%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+284}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right) + -4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]

Alternative 2: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+302} \lor \neg \left(t_1 \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right) + -4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \end{array} \end{array} \]

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 -2e+302) (not (<= t_1 5e+284)))
     (+ (* x (* 0.5 (/ y a))) (* -4.5 (* t (/ z a))))
     (/ 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 <= -2e+302) || !(t_1 <= 5e+284)) {
		tmp = (x * (0.5 * (y / a))) + (-4.5 * (t * (z / a)));
	} 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 <= (-2d+302)) .or. (.not. (t_1 <= 5d+284))) then
        tmp = (x * (0.5d0 * (y / a))) + ((-4.5d0) * (t * (z / a)))
    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 <= -2e+302) || !(t_1 <= 5e+284)) {
		tmp = (x * (0.5 * (y / a))) + (-4.5 * (t * (z / a)));
	} 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 <= -2e+302) or not (t_1 <= 5e+284):
		tmp = (x * (0.5 * (y / a))) + (-4.5 * (t * (z / a)))
	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 <= -2e+302) || !(t_1 <= 5e+284))
		tmp = Float64(Float64(x * Float64(0.5 * Float64(y / a))) + Float64(-4.5 * Float64(t * Float64(z / a))));
	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 <= -2e+302) || ~((t_1 <= 5e+284)))
		tmp = (x * (0.5 * (y / a))) + (-4.5 * (t * (z / a)));
	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, -2e+302], N[Not[LessEqual[t$95$1, 5e+284]], $MachinePrecision]], N[(N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $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 9) t)) < -2.0000000000000002e302 or 4.9999999999999999e284 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 70.4%

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

      1. associate-*l* 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in x around 0 68.8%

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

      1. fma-def 68.8%

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

      2. associate-/l* 82.0%

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

      3. associate-/l* 96.7%

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

   6. Simplified 96.7%

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

      1. fma-udef 96.8%

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

      2. associate-*r/ 96.8%

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

      3. +-commutative 96.8%

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

      4. *-commutative 96.8%

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

      5. div-inv 96.7%

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

      6. clear-num 96.8%

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

      7. associate-*l* 96.8%

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

      8. div-inv 96.8%

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

      9. clear-num 96.8%

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

      10. associate-*r* 96.7%

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

   8. Applied egg-rr 96.7%

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

   if -2.0000000000000002e302 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.9999999999999999e284

   1. Initial program 98.2%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{+302} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right) + -4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]

Alternative 3: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y - 9 \cdot \left(z \cdot t\right)}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) 5e+285)
   (/ 0.5 (/ a (- (* x y) (* 9.0 (* z t)))))
   (* 0.5 (/ y (/ a x)))))

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) <= 5e+285) {
		tmp = 0.5 / (a / ((x * y) - (9.0 * (z * t))));
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	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) <= 5d+285) then
        tmp = 0.5d0 / (a / ((x * y) - (9.0d0 * (z * t))))
    else
        tmp = 0.5d0 * (y / (a / x))
    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) <= 5e+285) {
		tmp = 0.5 / (a / ((x * y) - (9.0 * (z * t))));
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	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) <= 5e+285:
		tmp = 0.5 / (a / ((x * y) - (9.0 * (z * t))))
	else:
		tmp = 0.5 * (y / (a / x))
	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) <= 5e+285)
		tmp = Float64(0.5 / Float64(a / Float64(Float64(x * y) - Float64(9.0 * Float64(z * t)))));
	else
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	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) <= 5e+285)
		tmp = 0.5 / (a / ((x * y) - (9.0 * (z * t))));
	else
		tmp = 0.5 * (y / (a / x));
	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], 5e+285], N[(0.5 / N[(a / N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5.00000000000000016e285

   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* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in a around 0 93.3%

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

      1. associate-*r/ 93.3%

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

      2. cancel-sign-sub-inv 93.3%

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

      3. metadata-eval 93.3%

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

      4. +-commutative 93.3%

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

      5. associate-/l* 93.1%

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

      6. +-commutative 93.1%

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

      7. metadata-eval 93.1%

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

      8. cancel-sign-sub-inv 93.1%

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

      9. fma-neg 93.1%

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

      10. *-commutative 93.1%

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

      11. distribute-lft-neg-in 93.1%

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

      12. metadata-eval 93.1%

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

      13. *-commutative 93.1%

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

      14. associate-*l* 93.0%

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

   6. Simplified 93.0%

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

      1. *-commutative 93.0%

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

      2. metadata-eval 93.0%

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

      3. distribute-lft-neg-in 93.0%

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

      4. distribute-rgt-neg-in 93.0%

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

      5. fma-neg 93.0%

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

      6. associate-*r* 93.1%

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

      7. *-commutative 93.1%

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

      8. associate-*l* 93.1%

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

   8. Applied egg-rr 93.1%

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

   if 5.00000000000000016e285 < (*.f64 x y)

   1. Initial program 64.9%

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

      1. associate-*l* 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in x around inf 70.2%

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

      1. associate-*r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-/l* 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y - 9 \cdot \left(z \cdot t\right)}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 4: 93.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) 5e+285)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (* 0.5 (/ y (/ a x)))))

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) <= 5e+285) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	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) <= 5d+285) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (y / (a / x))
    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) <= 5e+285) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	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) <= 5e+285:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = 0.5 * (y / (a / x))
	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) <= 5e+285)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	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) <= 5e+285)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = 0.5 * (y / (a / x));
	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], 5e+285], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5.00000000000000016e285

   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* 93.3%

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

   3. Simplified 93.3%

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

   if 5.00000000000000016e285 < (*.f64 x y)

   1. Initial program 64.9%

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

      1. associate-*l* 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in x around inf 70.2%

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

      1. associate-*r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-/l* 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 5: 93.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) 5e+285)
   (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))
   (* 0.5 (/ y (/ a x)))))

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) <= 5e+285) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	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) <= 5d+285) then
        tmp = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (y / (a / x))
    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) <= 5e+285) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	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) <= 5e+285:
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0)
	else:
		tmp = 0.5 * (y / (a / x))
	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) <= 5e+285)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	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) <= 5e+285)
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	else
		tmp = 0.5 * (y / (a / x));
	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], 5e+285], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5.00000000000000016e285

   1. Initial program 93.3%

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

   if 5.00000000000000016e285 < (*.f64 x y)

   1. Initial program 64.9%

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

      1. associate-*l* 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in x around inf 70.2%

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

      1. associate-*r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-/l* 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 6: 68.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-103} \lor \neg \left(y \leq 2.4 \cdot 10^{+79}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

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 (<= y -2.5e-103) (not (<= y 2.4e+79)))
   (* 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 ((y <= -2.5e-103) || !(y <= 2.4e+79)) {
		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 ((y <= (-2.5d-103)) .or. (.not. (y <= 2.4d+79))) 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 ((y <= -2.5e-103) || !(y <= 2.4e+79)) {
		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 (y <= -2.5e-103) or not (y <= 2.4e+79):
		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 ((y <= -2.5e-103) || !(y <= 2.4e+79))
		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 ((y <= -2.5e-103) || ~((y <= 2.4e+79)))
		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[y, -2.5e-103], N[Not[LessEqual[y, 2.4e+79]], $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 y < -2.49999999999999983e-103 or 2.39999999999999986e79 < y

   1. Initial program 87.1%

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

      1. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in x around inf 62.2%

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

      1. associate-*r/ 68.9%

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

   6. Simplified 68.9%

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

   if -2.49999999999999983e-103 < y < 2.39999999999999986e79

   1. Initial program 95.3%

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

      1. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around 0 72.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-103} \lor \neg \left(y \leq 2.4 \cdot 10^{+79}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 7: 68.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+79}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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 (<= y -2.5e-103)
   (* 0.5 (* x (/ y a)))
   (if (<= y 2.4e+79) (* -4.5 (/ (* z t) a)) (* 0.5 (/ x (/ a y))))))

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 (y <= -2.5e-103) {
		tmp = 0.5 * (x * (y / a));
	} else if (y <= 2.4e+79) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	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 (y <= (-2.5d-103)) then
        tmp = 0.5d0 * (x * (y / a))
    else if (y <= 2.4d+79) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (x / (a / y))
    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 (y <= -2.5e-103) {
		tmp = 0.5 * (x * (y / a));
	} else if (y <= 2.4e+79) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.5e-103:
		tmp = 0.5 * (x * (y / a))
	elif y <= 2.4e+79:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (x / (a / y))
	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 (y <= -2.5e-103)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (y <= 2.4e+79)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	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 (y <= -2.5e-103)
		tmp = 0.5 * (x * (y / a));
	elseif (y <= 2.4e+79)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (x / (a / y));
	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[y, -2.5e-103], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+79], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999983e-103

   1. Initial program 89.2%

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

      1. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around inf 60.1%

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

      1. associate-*r/ 61.5%

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

   6. Simplified 61.5%

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

   if -2.49999999999999983e-103 < y < 2.39999999999999986e79

   1. Initial program 95.3%

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

      1. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around 0 72.5%

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

   if 2.39999999999999986e79 < y

   1. Initial program 84.3%

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

      1. associate-*l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in x around inf 65.0%

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

      1. associate-/l* 78.8%

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

   6. Simplified 78.8%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+79}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 68.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-103}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+79}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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 (<= y -2.4e-103)
   (* 0.5 (/ y (/ a x)))
   (if (<= y 1.05e+79) (* -4.5 (/ (* z t) a)) (* 0.5 (/ x (/ a y))))))

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 (y <= -2.4e-103) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 1.05e+79) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	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 (y <= (-2.4d-103)) then
        tmp = 0.5d0 * (y / (a / x))
    else if (y <= 1.05d+79) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (x / (a / y))
    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 (y <= -2.4e-103) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 1.05e+79) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.4e-103:
		tmp = 0.5 * (y / (a / x))
	elif y <= 1.05e+79:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (x / (a / y))
	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 (y <= -2.4e-103)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (y <= 1.05e+79)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	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 (y <= -2.4e-103)
		tmp = 0.5 * (y / (a / x));
	elseif (y <= 1.05e+79)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (x / (a / y));
	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[y, -2.4e-103], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+79], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000002e-103

   1. Initial program 89.2%

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

      1. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around inf 60.1%

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

      1. associate-*r/ 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in x around 0 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-/l* 63.2%

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

   9. Simplified 63.2%

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

   if -2.4000000000000002e-103 < y < 1.05000000000000004e79

   1. Initial program 95.3%

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

      1. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around 0 72.5%

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

   if 1.05000000000000004e79 < y

   1. Initial program 84.3%

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

      1. associate-*l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in x around inf 65.0%

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

      1. associate-/l* 78.8%

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

   6. Simplified 78.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-103}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+79}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \frac{t}{\frac{a}{z}} \end{array} \]

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 (/ a z))))

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 / (a / z));
}

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 / (a / z))
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 / (a / z));
}

Python

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

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(a / z)))
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 / (a / z));
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[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.2%

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

   1. associate-*l* 91.2%

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

3. Simplified 91.2%

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

4. Taylor expanded in x around 0 51.4%

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

   1. associate-/l* 52.0%

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

6. Simplified 52.0%

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

7. Final simplification 52.0%

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

Developer target: 93.2% accurate, 0.7× 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 2023322 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))