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

Percentage Accurate: 91.4% → 97.1%

Time: 7.7s

Alternatives: 12

Speedup: 0.8×

• 27.2% 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: 91.4% 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: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := y \cdot x - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+267}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) + -4.5 \cdot \left(\frac{t}{a} \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* y x) (* t (* z 9.0)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+267)))
     (+ (* 0.5 (* x (/ y a))) (* -4.5 (* (/ t a) z)))
     (/ t_1 (* a 2.0)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * x) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+267)) {
		tmp = (0.5 * (x * (y / a))) + (-4.5 * ((t / a) * z));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * x) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+267)) {
		tmp = (0.5 * (x * (y / a))) + (-4.5 * ((t / a) * z));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (y * x) - (t * (z * 9.0))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+267):
		tmp = (0.5 * (x * (y / a))) + (-4.5 * ((t / a) * z))
	else:
		tmp = t_1 / (a * 2.0)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * x) - Float64(t * Float64(z * 9.0)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+267))
		tmp = Float64(Float64(0.5 * Float64(x * Float64(y / a))) + Float64(-4.5 * Float64(Float64(t / a) * z)));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * x) - (t * (z * 9.0));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+267)))
		tmp = (0.5 * (x * (y / a))) + (-4.5 * ((t / a) * z));
	else
		tmp = t_1 / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+267]], $MachinePrecision]], N[(N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.5 * N[(N[(t / a), $MachinePrecision] * z), $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)) < -inf.0 or 4.9999999999999999e267 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 71.2%

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

      1. associate-*l* 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in x around 0 66.0%

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

      1. +-commutative 66.0%

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

      2. fma-def 66.0%

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

      3. associate-/l* 78.4%

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

      4. associate-/l* 93.3%

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

      5. associate-/r/ 93.3%

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

   6. Simplified 93.3%

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

      1. fma-udef 93.3%

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

      2. *-commutative 93.3%

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

      3. associate-/r/ 92.0%

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

      4. *-commutative 92.0%

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

   8. Applied egg-rr 92.0%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.9999999999999999e267

   1. Initial program 97.6%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x - t \cdot \left(z \cdot 9\right) \leq -\infty \lor \neg \left(y \cdot x - t \cdot \left(z \cdot 9\right) \leq 5 \cdot 10^{+267}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) + -4.5 \cdot \left(\frac{t}{a} \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 87.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{y}{\frac{a}{x}}, -4.5 \cdot \left(\frac{t}{a} \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y 4.8e-87)
   (fma 0.5 (/ y (/ a x)) (* -4.5 (* (/ t a) z)))
   (/ (fma x y (* -9.0 (* t z))) (* a 2.0))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.8e-87) {
		tmp = fma(0.5, (y / (a / x)), (-4.5 * ((t / a) * z)));
	} else {
		tmp = fma(x, y, (-9.0 * (t * z))) / (a * 2.0);
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 4.8e-87)
		tmp = fma(0.5, Float64(y / Float64(a / x)), Float64(-4.5 * Float64(Float64(t / a) * z)));
	else
		tmp = Float64(fma(x, y, Float64(-9.0 * Float64(t * z))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 4.8e-87], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(-4.5 * N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.7999999999999999e-87

   1. Initial program 87.6%

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

      1. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in x around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. fma-def 85.3%

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

      3. associate-/l* 87.1%

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

      4. associate-/l* 89.7%

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

      5. associate-/r/ 89.3%

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

   6. Simplified 89.3%

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

   if 4.7999999999999999e-87 < y

   1. Initial program 94.2%

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

      1. fma-neg 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-*l* 94.2%

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

      4. distribute-lft-neg-in 94.2%

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

      5. metadata-eval 94.2%

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

   3. Simplified 94.2%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{y}{\frac{a}{x}}, -4.5 \cdot \left(\frac{t}{a} \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}{a \cdot 2}\\ \end{array} \]

Alternative 3: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+121}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) + \frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.6e+121)
   (+ (* 0.5 (* x (/ y a))) (/ (* -4.5 t) (/ a z)))
   (/ (fma x y (* -9.0 (* t z))) (* a 2.0))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.6e+121) {
		tmp = (0.5 * (x * (y / a))) + ((-4.5 * t) / (a / z));
	} else {
		tmp = fma(x, y, (-9.0 * (t * z))) / (a * 2.0);
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.6e+121)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(y / a))) + Float64(Float64(-4.5 * t) / Float64(a / z)));
	else
		tmp = Float64(fma(x, y, Float64(-9.0 * Float64(t * z))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.6e+121], N[(N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.5 * t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e121

   1. Initial program 68.2%

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

      1. associate-*l* 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in x around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. fma-def 65.8%

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

      3. associate-/l* 86.0%

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

      4. associate-/l* 95.1%

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

      5. associate-/r/ 95.1%

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

   6. Simplified 95.1%

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

      1. fma-udef 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-/r/ 91.4%

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

      4. *-commutative 91.4%

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

   8. Applied egg-rr 91.4%

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

      1. associate-/r/ 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-*r/ 91.3%

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

   10. Applied egg-rr 91.3%

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

   if -1.6e121 < x

   1. Initial program 94.0%

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

      1. fma-neg 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-*l* 94.1%

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

      4. distribute-lft-neg-in 94.1%

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

      5. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+121}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) + \frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}{a \cdot 2}\\ \end{array} \]

Alternative 4: 93.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq 10^{+250}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) 1e+250)
   (/ (- (* y x) (* z (* t 9.0))) (* a 2.0))
   (* 0.5 (/ x (/ a y)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= 1e+250) {
		tmp = ((y * x) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 * x) <= 1d+250) then
        tmp = ((y * x) - (z * (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= 1e+250) {
		tmp = ((y * x) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= 1e+250:
		tmp = ((y * x) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= 1e+250)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= 1e+250)
		tmp = ((y * x) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], 1e+250], N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 9.9999999999999992e249

   1. Initial program 92.7%

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

      1. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   if 9.9999999999999992e249 < (*.f64 x y)

   1. Initial program 64.5%

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

      1. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 57.1%

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

      1. +-commutative 57.1%

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

      2. fma-def 57.1%

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

      3. associate-/l* 81.5%

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

      4. associate-/l* 88.8%

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

      5. associate-/r/ 88.8%

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

   6. Simplified 88.8%

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

      1. fma-udef 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-/r/ 88.8%

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

      4. *-commutative 88.8%

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

   8. Applied egg-rr 88.8%

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

   9. Taylor expanded in y around inf 68.5%

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

       1. *-commutative 68.5%

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

       2. associate-/l* 93.3%

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

   11. Simplified 93.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq 10^{+250}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 93.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq 10^{+250}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) 1e+250)
   (/ (- (* y x) (* t (* z 9.0))) (* a 2.0))
   (* 0.5 (/ x (/ a y)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= 1e+250) {
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 * x) <= 1d+250) then
        tmp = ((y * x) - (t * (z * 9.0d0))) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= 1e+250) {
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= 1e+250:
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= 1e+250)
		tmp = Float64(Float64(Float64(y * x) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= 1e+250)
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], 1e+250], N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 9.9999999999999992e249

   1. Initial program 92.7%

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

   if 9.9999999999999992e249 < (*.f64 x y)

   1. Initial program 64.5%

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

      1. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 57.1%

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

      1. +-commutative 57.1%

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

      2. fma-def 57.1%

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

      3. associate-/l* 81.5%

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

      4. associate-/l* 88.8%

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

      5. associate-/r/ 88.8%

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

   6. Simplified 88.8%

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

      1. fma-udef 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-/r/ 88.8%

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

      4. *-commutative 88.8%

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

   8. Applied egg-rr 88.8%

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

   9. Taylor expanded in y around inf 68.5%

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

       1. *-commutative 68.5%

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

       2. associate-/l* 93.3%

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

   11. Simplified 93.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq 10^{+250}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 90.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+114}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) + \frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4e+114)
   (+ (* 0.5 (* x (/ y a))) (/ (* -4.5 t) (/ a z)))
   (/ (- (* y x) (* t (* z 9.0))) (* a 2.0))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e+114) {
		tmp = (0.5 * (x * (y / a))) + ((-4.5 * t) / (a / z));
	} else {
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: z and t 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 <= (-4d+114)) then
        tmp = (0.5d0 * (x * (y / a))) + (((-4.5d0) * t) / (a / z))
    else
        tmp = ((y * x) - (t * (z * 9.0d0))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e+114) {
		tmp = (0.5 * (x * (y / a))) + ((-4.5 * t) / (a / z));
	} else {
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -4e+114:
		tmp = (0.5 * (x * (y / a))) + ((-4.5 * t) / (a / z))
	else:
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4e+114)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(y / a))) + Float64(Float64(-4.5 * t) / Float64(a / z)));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4e+114)
		tmp = (0.5 * (x * (y / a))) + ((-4.5 * t) / (a / z));
	else
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4e+114], N[(N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.5 * t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4e114

   1. Initial program 68.2%

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

      1. associate-*l* 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in x around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. fma-def 65.8%

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

      3. associate-/l* 86.0%

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

      4. associate-/l* 95.1%

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

      5. associate-/r/ 95.1%

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

   6. Simplified 95.1%

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

      1. fma-udef 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-/r/ 91.4%

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

      4. *-commutative 91.4%

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

   8. Applied egg-rr 91.4%

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

      1. associate-/r/ 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-*r/ 91.3%

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

   10. Applied egg-rr 91.3%

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

   if -4e114 < x

   1. Initial program 94.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+114}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right) + \frac{-4.5 \cdot t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 7: 66.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-104} \lor \neg \left(t \leq 8 \cdot 10^{+22}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e-104) (not (<= t 8e+22)))
   (* -4.5 (/ t (/ a z)))
   (* 0.5 (/ x (/ a y)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e-104) || !(t <= 8e+22)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 ((t <= (-2.3d-104)) .or. (.not. (t <= 8d+22))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e-104) || !(t <= 8e+22)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e-104) or not (t <= 8e+22):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e-104) || !(t <= 8e+22))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e-104) || ~((t <= 8e+22)))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e-104], N[Not[LessEqual[t, 8e+22]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2999999999999999e-104 or 8e22 < t

   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 64.4%

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

      1. associate-/l* 68.2%

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

   6. Simplified 68.2%

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

   if -2.2999999999999999e-104 < t < 8e22

   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 x around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. fma-def 93.3%

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

      3. associate-/l* 90.8%

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

      4. associate-/l* 88.7%

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

      5. associate-/r/ 89.8%

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

   6. Simplified 89.8%

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

      1. fma-udef 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-/r/ 96.2%

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

      4. *-commutative 96.2%

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

   8. Applied egg-rr 96.2%

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

   9. Taylor expanded in y around inf 73.2%

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

       1. *-commutative 73.2%

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

       2. associate-/l* 76.9%

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

   11. Simplified 76.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-104} \lor \neg \left(t \leq 8 \cdot 10^{+22}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 66.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-98} \lor \neg \left(t \leq 1.6 \cdot 10^{+22}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e-98) (not (<= t 1.6e+22)))
   (* -4.5 (/ t (/ a z)))
   (* 0.5 (/ y (/ a x)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e-98) || !(t <= 1.6e+22)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 ((t <= (-9.5d-98)) .or. (.not. (t <= 1.6d+22))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = 0.5d0 * (y / (a / x))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e-98) || !(t <= 1.6e+22)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.5e-98) or not (t <= 1.6e+22):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = 0.5 * (y / (a / x))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e-98) || !(t <= 1.6e+22))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.5e-98) || ~((t <= 1.6e+22)))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = 0.5 * (y / (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.5e-98], N[Not[LessEqual[t, 1.6e+22]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5000000000000001e-98 or 1.6e22 < t

   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 64.4%

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

      1. associate-/l* 68.2%

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

   6. Simplified 68.2%

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

   if -9.5000000000000001e-98 < t < 1.6e22

   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 x around inf 73.2%

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

      1. associate-/l* 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-98} \lor \neg \left(t \leq 1.6 \cdot 10^{+22}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 9: 67.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-108} \lor \neg \left(t \leq 5.8 \cdot 10^{+67}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.8e-108) (not (<= t 5.8e+67)))
   (* -4.5 (/ t (/ a z)))
   (* y (* x (/ 0.5 a)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e-108) || !(t <= 5.8e+67)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = y * (x * (0.5 / a));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 ((t <= (-3.8d-108)) .or. (.not. (t <= 5.8d+67))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = y * (x * (0.5d0 / a))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e-108) || !(t <= 5.8e+67)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = y * (x * (0.5 / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.8e-108) or not (t <= 5.8e+67):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = y * (x * (0.5 / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.8e-108) || !(t <= 5.8e+67))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.8e-108) || ~((t <= 5.8e+67)))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = y * (x * (0.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.8e-108], N[Not[LessEqual[t, 5.8e+67]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.79999999999999973e-108 or 5.80000000000000047e67 < t

   1. Initial program 87.0%

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

      1. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in x around 0 64.8%

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

      1. associate-/l* 68.6%

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

   6. Simplified 68.6%

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

   if -3.79999999999999973e-108 < t < 5.80000000000000047e67

   1. Initial program 93.6%

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

      1. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around 0 93.5%

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

      1. +-commutative 93.5%

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

      2. fma-def 93.5%

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

      3. associate-/l* 91.1%

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

      4. associate-/l* 89.1%

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

      5. associate-/r/ 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in y around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r/ 72.4%

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

      4. associate-*l* 71.7%

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

   9. Simplified 71.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-108} \lor \neg \left(t \leq 5.8 \cdot 10^{+67}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \end{array} \]

Alternative 10: 67.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-100}:\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e-100)
   (* (* -4.5 t) (/ z a))
   (if (<= t 1.3e+68) (* y (* x (/ 0.5 a))) (* -4.5 (/ t (/ a z))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-100) {
		tmp = (-4.5 * t) * (z / a);
	} else if (t <= 1.3e+68) {
		tmp = y * (x * (0.5 / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 (t <= (-1.2d-100)) then
        tmp = ((-4.5d0) * t) * (z / a)
    else if (t <= 1.3d+68) then
        tmp = y * (x * (0.5d0 / a))
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-100) {
		tmp = (-4.5 * t) * (z / a);
	} else if (t <= 1.3e+68) {
		tmp = y * (x * (0.5 / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e-100:
		tmp = (-4.5 * t) * (z / a)
	elif t <= 1.3e+68:
		tmp = y * (x * (0.5 / a))
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e-100)
		tmp = Float64(Float64(-4.5 * t) * Float64(z / a));
	elseif (t <= 1.3e+68)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e-100)
		tmp = (-4.5 * t) * (z / a);
	elseif (t <= 1.3e+68)
		tmp = y * (x * (0.5 / a));
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e-100], N[(N[(-4.5 * t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+68], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2000000000000001e-100

   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 0 87.5%

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

      1. +-commutative 87.5%

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

      2. fma-def 87.5%

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

      3. associate-/l* 87.4%

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

      4. associate-/l* 92.9%

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

      5. associate-/r/ 90.6%

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

   6. Simplified 90.6%

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

      1. fma-udef 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-/r/ 87.2%

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

      4. *-commutative 87.2%

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

   8. Applied egg-rr 87.2%

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

   9. Taylor expanded in y around 0 63.7%

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

       1. associate-*r/ 66.7%

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

       2. associate-*r* 66.7%

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

   11. Simplified 66.7%

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

   if -1.2000000000000001e-100 < t < 1.2999999999999999e68

   1. Initial program 93.6%

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

      1. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around 0 93.5%

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

      1. +-commutative 93.5%

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

      2. fma-def 93.5%

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

      3. associate-/l* 91.1%

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

      4. associate-/l* 89.1%

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

      5. associate-/r/ 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in y around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r/ 72.4%

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

      4. associate-*l* 71.7%

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

   9. Simplified 71.7%

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

   if 1.2999999999999999e68 < t

   1. Initial program 79.9%

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

      1. associate-*l* 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in x around 0 66.2%

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

      1. associate-/l* 72.3%

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

   6. Simplified 72.3%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-100}:\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 50.9% accurate, 1.9× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

   1. associate-*l* 89.8%

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

3. Simplified 89.8%

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

4. Taylor expanded in x around 0 52.8%

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

   1. associate-/l* 55.4%

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

   2. associate-/r/ 53.9%

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

6. Simplified 53.9%

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

7. Final simplification 53.9%

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

Alternative 12: 50.8% accurate, 1.9× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t 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 89.8%

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

   1. associate-*l* 89.8%

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

3. Simplified 89.8%

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

4. Taylor expanded in x around 0 52.8%

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

   1. associate-/l* 55.4%

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

6. Simplified 55.4%

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

7. Final simplification 55.4%

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

Developer target: 93.1% 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 2023268 
(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)))