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

Percentage Accurate: 91.2% → 94.7%

Time: 8.6s

Alternatives: 11

Speedup: 0.8×

• 28.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{+53} \lor \neg \left(a \cdot 2 \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot \frac{0.5}{a}, \frac{z}{a} \cdot \left(0.5 \cdot \left(t \cdot \left(-9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 2.0) -1e+53) (not (<= (* a 2.0) 5e-44)))
   (fma x (* y (/ 0.5 a)) (* (/ z a) (* 0.5 (* t (- 9.0)))))
   (/ (fma x y (* -9.0 (* z t))) (* a 2.0))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 2.0) <= -1e+53) || !((a * 2.0) <= 5e-44)) {
		tmp = fma(x, (y * (0.5 / a)), ((z / a) * (0.5 * (t * -9.0))));
	} else {
		tmp = fma(x, y, (-9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 2.0) <= -1e+53) || !(Float64(a * 2.0) <= 5e-44))
		tmp = fma(x, Float64(y * Float64(0.5 / a)), Float64(Float64(z / a) * Float64(0.5 * Float64(t * Float64(-9.0)))));
	else
		tmp = Float64(fma(x, y, Float64(-9.0 * Float64(z * t))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 2.0), $MachinePrecision], -1e+53], N[Not[LessEqual[N[(a * 2.0), $MachinePrecision], 5e-44]], $MachinePrecision]], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * N[(0.5 * N[(t * (-9.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < -9.9999999999999999e52 or 5.00000000000000039e-44 < (*.f64 a 2)

   1. Initial program 79.6%

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

      1. associate-*l* 79.6%

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

   3. Simplified 79.6%

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

      1. div-sub 79.6%

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

      2. div-inv 79.6%

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

      3. *-commutative 79.6%

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

      4. associate-/r* 79.6%

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

      5. metadata-eval 79.6%

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

      6. times-frac 88.6%

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

   5. Applied egg-rr 88.6%

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

      1. cancel-sign-sub-inv 88.6%

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

      2. associate-*l* 96.7%

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

      3. fma-def 96.7%

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

      4. div-inv 96.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot \frac{0.5}{a}, \left(-\frac{z}{a}\right) \cdot \color{blue}{\left(\left(9 \cdot t\right) \cdot \frac{1}{2}\right)}\right) \]

      5. *-commutative 96.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot \frac{0.5}{a}, \left(-\frac{z}{a}\right) \cdot \left(\color{blue}{\left(t \cdot 9\right)} \cdot \frac{1}{2}\right)\right) \]

      6. metadata-eval 96.7%

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

   7. Applied egg-rr 96.7%

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

   if -9.9999999999999999e52 < (*.f64 a 2) < 5.00000000000000039e-44

   1. Initial program 95.1%

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

      1. fma-neg 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-*l* 96.7%

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

      4. distribute-lft-neg-in 96.7%

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

      5. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{+53} \lor \neg \left(a \cdot 2 \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot \frac{0.5}{a}, \frac{z}{a} \cdot \left(0.5 \cdot \left(t \cdot \left(-9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 92.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 56.4%

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

      1. associate-*l* 56.4%

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

   3. Simplified 56.4%

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

      1. div-sub 48.7%

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

      2. div-inv 48.7%

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

      3. *-commutative 48.7%

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

      4. associate-/r* 48.7%

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

      5. metadata-eval 48.7%

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

      6. times-frac 85.0%

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

   5. Applied egg-rr 85.0%

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

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

   1. Initial program 90.8%

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

      1. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

      1. div-inv 90.8%

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

      2. fma-neg 92.1%

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

      3. distribute-rgt-neg-in 92.1%

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

      4. *-commutative 92.1%

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

      5. distribute-rgt-neg-in 92.1%

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

      6. metadata-eval 92.1%

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

      7. *-commutative 92.1%

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

      8. associate-/r* 92.1%

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

      9. metadata-eval 92.1%

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

   5. Applied egg-rr 92.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

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

Alternative 3: 92.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -1 \cdot 10^{+217}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right) - \frac{z}{a} \cdot \frac{t \cdot 9}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* t (* z 9.0))) -1e+217)
   (- (* (/ 0.5 a) (* x y)) (* (/ z a) (/ (* t 9.0) 2.0)))
   (/ (fma x y (* -9.0 (* z t))) (* a 2.0))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - (t * (z * 9.0))) <= -1e+217) {
		tmp = ((0.5 / a) * (x * y)) - ((z / a) * ((t * 9.0) / 2.0));
	} else {
		tmp = fma(x, y, (-9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) <= -1e+217)
		tmp = Float64(Float64(Float64(0.5 / a) * Float64(x * y)) - Float64(Float64(z / a) * Float64(Float64(t * 9.0) / 2.0)));
	else
		tmp = Float64(fma(x, y, Float64(-9.0 * Float64(z * t))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1e+217], N[(N[(N[(0.5 / a), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * N[(N[(t * 9.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -9.9999999999999996e216

   1. Initial program 70.1%

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

      1. associate-*l* 70.1%

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

   3. Simplified 70.1%

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

      1. div-sub 64.8%

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

      2. div-inv 64.8%

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

      3. *-commutative 64.8%

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

      4. associate-/r* 64.8%

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

      5. metadata-eval 64.8%

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

      6. times-frac 86.9%

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

   5. Applied egg-rr 86.9%

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

   if -9.9999999999999996e216 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 90.3%

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

      1. fma-neg 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*l* 91.7%

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

      4. distribute-lft-neg-in 91.7%

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

      5. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -1 \cdot 10^{+217}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right) - \frac{z}{a} \cdot \frac{t \cdot 9}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \end{array} \]

Alternative 4: 93.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 9\right)\\ t_2 := t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y - t_1}{a \cdot 2}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-251}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+219}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (* z 9.0))) (t_2 (* t (* (/ z a) -4.5))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e-222)
       (/ (- (* x y) t_1) (* a 2.0))
       (if (<= t_1 2e-251)
         (* (* x 0.5) (/ y a))
         (if (<= t_1 5e+219)
           (+ (* -4.5 (/ (* z t) a)) (* 0.5 (/ (* x y) a)))
           t_2))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * 9.0);
	double t_2 = t * ((z / a) * -4.5);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e-222) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else if (t_1 <= 2e-251) {
		tmp = (x * 0.5) * (y / a);
	} else if (t_1 <= 5e+219) {
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * ((x * y) / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * 9.0);
	double t_2 = t * ((z / a) * -4.5);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -5e-222) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else if (t_1 <= 2e-251) {
		tmp = (x * 0.5) * (y / a);
	} else if (t_1 <= 5e+219) {
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * ((x * y) / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = t * (z * 9.0)
	t_2 = t * ((z / a) * -4.5)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -5e-222:
		tmp = ((x * y) - t_1) / (a * 2.0)
	elif t_1 <= 2e-251:
		tmp = (x * 0.5) * (y / a)
	elif t_1 <= 5e+219:
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * ((x * y) / a))
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z * 9.0))
	t_2 = Float64(t * Float64(Float64(z / a) * -4.5))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -5e-222)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	elseif (t_1 <= 2e-251)
		tmp = Float64(Float64(x * 0.5) * Float64(y / a));
	elseif (t_1 <= 5e+219)
		tmp = Float64(Float64(-4.5 * Float64(Float64(z * t) / a)) + Float64(0.5 * Float64(Float64(x * y) / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z * 9.0);
	t_2 = t * ((z / a) * -4.5);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -5e-222)
		tmp = ((x * y) - t_1) / (a * 2.0);
	elseif (t_1 <= 2e-251)
		tmp = (x * 0.5) * (y / a);
	elseif (t_1 <= 5e+219)
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * ((x * y) / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e-222], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-251], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+219], N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 z 9) t) < -inf.0 or 5e219 < (*.f64 (*.f64 z 9) t)

   1. Initial program 53.3%

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

      1. associate-*l* 53.2%

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

   3. Simplified 53.2%

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

      1. div-inv 53.2%

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

      2. fma-neg 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. *-commutative 60.2%

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

      5. distribute-rgt-neg-in 60.2%

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

      6. metadata-eval 60.2%

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

      7. *-commutative 60.2%

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

      8. associate-/r* 60.2%

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

      9. metadata-eval 60.2%

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

   5. Applied egg-rr 60.2%

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

   6. Taylor expanded in x around 0 60.2%

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

      1. associate-*r/ 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*l* 92.9%

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

      4. *-commutative 92.9%

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

   8. Simplified 92.9%

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

   if -inf.0 < (*.f64 (*.f64 z 9) t) < -5.00000000000000008e-222

   1. Initial program 97.5%

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

   if -5.00000000000000008e-222 < (*.f64 (*.f64 z 9) t) < 2.00000000000000003e-251

   1. Initial program 83.7%

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

      1. associate-*l* 83.7%

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

   3. Simplified 83.7%

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

      1. div-inv 83.6%

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

      2. fma-neg 83.6%

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

      3. distribute-rgt-neg-in 83.6%

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

      4. *-commutative 83.6%

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

      5. distribute-rgt-neg-in 83.6%

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

      6. metadata-eval 83.6%

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

      7. *-commutative 83.6%

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

      8. associate-/r* 83.6%

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

      9. metadata-eval 83.6%

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

   5. Applied egg-rr 83.6%

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

   6. Taylor expanded in x around inf 81.8%

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

      1. associate-*r/ 81.9%

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

   8. Applied egg-rr 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*r* 81.9%

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

      3. *-un-lft-identity 81.9%

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

      4. times-frac 93.1%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{1} \cdot \frac{y}{a}} \]

   10. Applied egg-rr 93.1%

       \[\leadsto \color{blue}{\frac{0.5 \cdot x}{1} \cdot \frac{y}{a}} \]

   if 2.00000000000000003e-251 < (*.f64 (*.f64 z 9) t) < 5e219

   1. Initial program 96.0%

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

      1. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around 0 96.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq -\infty:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq -5 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{-251}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 5 \cdot 10^{+219}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \end{array} \]

Alternative 5: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 9\right)\\ t_2 := t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y - t_1}{a \cdot 2}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-251}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+219}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (* z 9.0))) (t_2 (* t (* (/ z a) -4.5))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e-222)
       (/ (- (* x y) t_1) (* a 2.0))
       (if (<= t_1 2e-251)
         (* (* x 0.5) (/ y a))
         (if (<= t_1 5e+219)
           (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
           t_2))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * 9.0);
	double t_2 = t * ((z / a) * -4.5);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e-222) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else if (t_1 <= 2e-251) {
		tmp = (x * 0.5) * (y / a);
	} else if (t_1 <= 5e+219) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * 9.0);
	double t_2 = t * ((z / a) * -4.5);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -5e-222) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else if (t_1 <= 2e-251) {
		tmp = (x * 0.5) * (y / a);
	} else if (t_1 <= 5e+219) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = t * (z * 9.0)
	t_2 = t * ((z / a) * -4.5)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -5e-222:
		tmp = ((x * y) - t_1) / (a * 2.0)
	elif t_1 <= 2e-251:
		tmp = (x * 0.5) * (y / a)
	elif t_1 <= 5e+219:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z * 9.0))
	t_2 = Float64(t * Float64(Float64(z / a) * -4.5))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -5e-222)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	elseif (t_1 <= 2e-251)
		tmp = Float64(Float64(x * 0.5) * Float64(y / a));
	elseif (t_1 <= 5e+219)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z * 9.0);
	t_2 = t * ((z / a) * -4.5);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -5e-222)
		tmp = ((x * y) - t_1) / (a * 2.0);
	elseif (t_1 <= 2e-251)
		tmp = (x * 0.5) * (y / a);
	elseif (t_1 <= 5e+219)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e-222], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-251], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+219], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 z 9) t) < -inf.0 or 5e219 < (*.f64 (*.f64 z 9) t)

   1. Initial program 53.3%

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

      1. associate-*l* 53.2%

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

   3. Simplified 53.2%

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

      1. div-inv 53.2%

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

      2. fma-neg 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. *-commutative 60.2%

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

      5. distribute-rgt-neg-in 60.2%

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

      6. metadata-eval 60.2%

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

      7. *-commutative 60.2%

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

      8. associate-/r* 60.2%

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

      9. metadata-eval 60.2%

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

   5. Applied egg-rr 60.2%

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

   6. Taylor expanded in x around 0 60.2%

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

      1. associate-*r/ 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*l* 92.9%

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

      4. *-commutative 92.9%

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

   8. Simplified 92.9%

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

   if -inf.0 < (*.f64 (*.f64 z 9) t) < -5.00000000000000008e-222

   1. Initial program 97.5%

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

   if -5.00000000000000008e-222 < (*.f64 (*.f64 z 9) t) < 2.00000000000000003e-251

   1. Initial program 83.7%

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

      1. associate-*l* 83.7%

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

   3. Simplified 83.7%

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

      1. div-inv 83.6%

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

      2. fma-neg 83.6%

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

      3. distribute-rgt-neg-in 83.6%

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

      4. *-commutative 83.6%

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

      5. distribute-rgt-neg-in 83.6%

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

      6. metadata-eval 83.6%

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

      7. *-commutative 83.6%

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

      8. associate-/r* 83.6%

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

      9. metadata-eval 83.6%

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

   5. Applied egg-rr 83.6%

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

   6. Taylor expanded in x around inf 81.8%

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

      1. associate-*r/ 81.9%

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

   8. Applied egg-rr 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*r* 81.9%

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

      3. *-un-lft-identity 81.9%

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

      4. times-frac 93.1%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{1} \cdot \frac{y}{a}} \]

   10. Applied egg-rr 93.1%

       \[\leadsto \color{blue}{\frac{0.5 \cdot x}{1} \cdot \frac{y}{a}} \]

   if 2.00000000000000003e-251 < (*.f64 (*.f64 z 9) t) < 5e219

   1. Initial program 96.0%

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

      1. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq -\infty:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq -5 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{-251}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 5 \cdot 10^{+219}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \end{array} \]

Alternative 6: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 5e+298)
   (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
   (* 0.5 (* y (/ x a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 5e+298) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Fortran

NOTE: x and y 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+298) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (y * (x / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 5e+298) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 5e+298:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 5e+298)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 5e+298)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 5e+298], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5.0000000000000003e298

   1. Initial program 90.2%

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

      1. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   if 5.0000000000000003e298 < (*.f64 x y)

   1. Initial program 56.9%

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

      1. associate-*l* 56.9%

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

   3. Simplified 56.9%

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

   4. Taylor expanded in x around inf 61.4%

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

      1. associate-/l* 95.3%

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

      2. associate-/r/ 95.5%

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

   6. Simplified 95.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 7: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ t_2 := -4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (* y (/ x a)))) (t_2 (* -4.5 (/ t (/ a z)))))
   (if (<= z -2.05e+101)
     t_2
     (if (<= z -8.5e+59)
       t_1
       (if (<= z -2.5e+49)
         (* -4.5 (/ (* z t) a))
         (if (<= z 4e-43) t_1 t_2))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y * (x / a));
	double t_2 = -4.5 * (t / (a / z));
	double tmp;
	if (z <= -2.05e+101) {
		tmp = t_2;
	} else if (z <= -8.5e+59) {
		tmp = t_1;
	} else if (z <= -2.5e+49) {
		tmp = -4.5 * ((z * t) / a);
	} else if (z <= 4e-43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 = 0.5d0 * (y * (x / a))
    t_2 = (-4.5d0) * (t / (a / z))
    if (z <= (-2.05d+101)) then
        tmp = t_2
    else if (z <= (-8.5d+59)) then
        tmp = t_1
    else if (z <= (-2.5d+49)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (z <= 4d-43) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y * (x / a));
	double t_2 = -4.5 * (t / (a / z));
	double tmp;
	if (z <= -2.05e+101) {
		tmp = t_2;
	} else if (z <= -8.5e+59) {
		tmp = t_1;
	} else if (z <= -2.5e+49) {
		tmp = -4.5 * ((z * t) / a);
	} else if (z <= 4e-43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = 0.5 * (y * (x / a))
	t_2 = -4.5 * (t / (a / z))
	tmp = 0
	if z <= -2.05e+101:
		tmp = t_2
	elif z <= -8.5e+59:
		tmp = t_1
	elif z <= -2.5e+49:
		tmp = -4.5 * ((z * t) / a)
	elif z <= 4e-43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(y * Float64(x / a)))
	t_2 = Float64(-4.5 * Float64(t / Float64(a / z)))
	tmp = 0.0
	if (z <= -2.05e+101)
		tmp = t_2;
	elseif (z <= -8.5e+59)
		tmp = t_1;
	elseif (z <= -2.5e+49)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (z <= 4e-43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (y * (x / a));
	t_2 = -4.5 * (t / (a / z));
	tmp = 0.0;
	if (z <= -2.05e+101)
		tmp = t_2;
	elseif (z <= -8.5e+59)
		tmp = t_1;
	elseif (z <= -2.5e+49)
		tmp = -4.5 * ((z * t) / a);
	elseif (z <= 4e-43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+101], t$95$2, If[LessEqual[z, -8.5e+59], t$95$1, If[LessEqual[z, -2.5e+49], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-43], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e101 or 4.00000000000000031e-43 < z

   1. Initial program 82.6%

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

      1. associate-*l* 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in x around 0 62.8%

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

      1. associate-/l* 73.5%

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

   6. Simplified 73.5%

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

   if -2.05e101 < z < -8.4999999999999999e59 or -2.5000000000000002e49 < z < 4.00000000000000031e-43

   1. Initial program 92.1%

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

      1. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. associate-/l* 66.2%

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

      2. associate-/r/ 69.5%

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

   6. Simplified 69.5%

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

   if -8.4999999999999999e59 < z < -2.5000000000000002e49

   1. Initial program 80.7%

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

      1. associate-*l* 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in x around 0 61.5%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+101}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+59}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-43}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+67} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+67) (not (<= (* x y) 5e-13)))
   (* 0.5 (/ x (/ a y)))
   (* -4.5 (/ t (/ a z)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+67) || !((x * y) <= 5e-13)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x and y 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+67)) .or. (.not. ((x * y) <= 5d-13))) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+67) || !((x * y) <= 5e-13)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e+67) or not ((x * y) <= 5e-13):
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+67) || !(Float64(x * y) <= 5e-13))
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e+67) || ~(((x * y) <= 5e-13)))
		tmp = 0.5 * (x / (a / y));
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+67], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-13]], $MachinePrecision]], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999976e67 or 4.9999999999999999e-13 < (*.f64 x y)

   1. Initial program 84.7%

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

      1. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 70.4%

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

      1. associate-/l* 77.7%

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

   6. Simplified 77.7%

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

   if -4.99999999999999976e67 < (*.f64 x y) < 4.9999999999999999e-13

   1. Initial program 89.7%

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

      1. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around 0 71.6%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+67} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+67}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+67)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* x y) 5e-13) (* -4.5 (/ t (/ a z))) (* (* x 0.5) (/ y a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+67) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 5e-13) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (x * 0.5) * (y / a);
	}
	return tmp;
}

Fortran

NOTE: x and y 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+67)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((x * y) <= 5d-13) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (x * 0.5d0) * (y / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+67) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 5e-13) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (x * 0.5) * (y / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+67:
		tmp = 0.5 * (x / (a / y))
	elif (x * y) <= 5e-13:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = (x * 0.5) * (y / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+67)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(x * y) <= 5e-13)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(Float64(x * 0.5) * Float64(y / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+67)
		tmp = 0.5 * (x / (a / y));
	elseif ((x * y) <= 5e-13)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = (x * 0.5) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+67], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-13], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.99999999999999976e67

   1. Initial program 82.8%

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

      1. associate-*l* 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in x around inf 78.5%

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

      1. associate-/l* 82.7%

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

   6. Simplified 82.7%

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

   if -4.99999999999999976e67 < (*.f64 x y) < 4.9999999999999999e-13

   1. Initial program 89.7%

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

      1. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around 0 71.6%

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

      1. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

   if 4.9999999999999999e-13 < (*.f64 x y)

   1. Initial program 85.9%

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

      1. associate-*l* 85.9%

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

   3. Simplified 85.9%

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

      1. div-inv 85.9%

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

      2. fma-neg 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

      4. *-commutative 87.2%

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

      5. distribute-rgt-neg-in 87.2%

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

      6. metadata-eval 87.2%

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

      7. *-commutative 87.2%

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

      8. associate-/r* 87.2%

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

      9. metadata-eval 87.2%

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

   5. Applied egg-rr 87.2%

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

   6. Taylor expanded in x around inf 65.7%

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

      1. associate-*r/ 65.6%

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

   8. Applied egg-rr 65.6%

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

      1. *-commutative 65.6%

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

      2. associate-*r* 65.6%

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

      3. *-un-lft-identity 65.6%

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

      4. times-frac 74.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{1} \cdot \frac{y}{a}} \]

   10. Applied egg-rr 74.3%

       \[\leadsto \color{blue}{\frac{0.5 \cdot x}{1} \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+67}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 52.0% accurate, 1.9× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (* z (/ t a))))

C

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

Fortran

NOTE: x and y 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) * (z * (t / a))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (z * (t / a));
end

Wolfram

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

Derivation

1. Initial program 87.3%

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

   1. associate-*l* 87.3%

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

3. Simplified 87.3%

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

4. Taylor expanded in x around 0 49.9%

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

   1. associate-/l* 54.4%

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

6. Simplified 54.4%

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

   1. associate-/r/ 51.9%

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

8. Applied egg-rr 51.9%

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

9. Final simplification 51.9%

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

Alternative 11: 51.7% accurate, 1.9× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t / (a / z));
end

Wolfram

NOTE: x and y 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 87.3%

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

   1. associate-*l* 87.3%

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

3. Simplified 87.3%

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

4. Taylor expanded in x around 0 49.9%

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

   1. associate-/l* 54.4%

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

6. Simplified 54.4%

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

7. Final simplification 54.4%

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

Developer target: 93.4% 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 2023297 
(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)))