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

Percentage Accurate: 90.9% → 94.2%

Time: 9.4s

Alternatives: 13

Speedup: 0.8×

• 28.5% 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: 90.9% 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: 94.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(0.5, t_1, \frac{t}{\frac{\frac{a}{z}}{-4.5}}\right)\\ \mathbf{elif}\;a \cdot 2 \leq 5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.5, t_1, -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ a y))))
   (if (<= (* a 2.0) -1e+162)
     (fma 0.5 t_1 (/ t (/ (/ a z) -4.5)))
     (if (<= (* a 2.0) 5e+28)
       (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))
       (fma 0.5 t_1 (* -4.5 (* z (/ t a))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double tmp;
	if ((a * 2.0) <= -1e+162) {
		tmp = fma(0.5, t_1, (t / ((a / z) / -4.5)));
	} else if ((a * 2.0) <= 5e+28) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = fma(0.5, t_1, (-4.5 * (z * (t / a))));
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	tmp = 0.0
	if (Float64(a * 2.0) <= -1e+162)
		tmp = fma(0.5, t_1, Float64(t / Float64(Float64(a / z) / -4.5)));
	elseif (Float64(a * 2.0) <= 5e+28)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = fma(0.5, t_1, Float64(-4.5 * Float64(z * Float64(t / a))));
	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_] := Block[{t$95$1 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 2.0), $MachinePrecision], -1e+162], N[(0.5 * t$95$1 + N[(t / N[(N[(a / z), $MachinePrecision] / -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 2.0), $MachinePrecision], 5e+28], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * t$95$1 + N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 2) < -9.9999999999999994e161

   1. Initial program 74.7%

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

      1. *-commutative 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*l* 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in x around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. fma-def 74.8%

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

      3. associate-/l* 79.3%

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

      4. associate-/l* 98.9%

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

      5. associate-/r/ 84.2%

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

   6. Simplified 84.2%

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

      1. associate-*r* 84.1%

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

      2. associate-*r/ 84.1%

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

      3. associate-/r/ 98.9%

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

      4. *-commutative 98.9%

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

      5. associate-/l* 99.0%

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

   8. Applied egg-rr 99.0%

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

   if -9.9999999999999994e161 < (*.f64 a 2) < 4.99999999999999957e28

   1. Initial program 98.2%

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

   if 4.99999999999999957e28 < (*.f64 a 2)

   1. Initial program 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

      3. associate-*l* 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in x around 0 75.0%

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

      1. +-commutative 75.0%

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

      2. fma-def 75.0%

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

      3. associate-/l* 86.5%

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

      4. associate-/l* 92.3%

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

      5. associate-/r/ 98.2%

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

   6. Simplified 98.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{x}{\frac{a}{y}}, \frac{t}{\frac{\frac{a}{z}}{-4.5}}\right)\\ \mathbf{elif}\;a \cdot 2 \leq 5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{x}{\frac{a}{y}}, -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\right)\\ \end{array} \]

Alternative 2: 94.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -2 \cdot 10^{+178}:\\ \;\;\;\;t \cdot \frac{z}{a \cdot -0.2222222222222222} + 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;a \cdot 2 \leq 5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{x}{\frac{a}{y}}, -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) -2e+178)
   (+ (* t (/ z (* a -0.2222222222222222))) (* 0.5 (* x (/ y a))))
   (if (<= (* a 2.0) 5e+28)
     (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))
     (fma 0.5 (/ x (/ a y)) (* -4.5 (* z (/ t a)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -2e+178) {
		tmp = (t * (z / (a * -0.2222222222222222))) + (0.5 * (x * (y / a)));
	} else if ((a * 2.0) <= 5e+28) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = fma(0.5, (x / (a / y)), (-4.5 * (z * (t / a))));
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -2e+178)
		tmp = Float64(Float64(t * Float64(z / Float64(a * -0.2222222222222222))) + Float64(0.5 * Float64(x * Float64(y / a))));
	elseif (Float64(a * 2.0) <= 5e+28)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = fma(0.5, Float64(x / Float64(a / y)), Float64(-4.5 * Float64(z * Float64(t / a))));
	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[N[(a * 2.0), $MachinePrecision], -2e+178], N[(N[(t * N[(z / N[(a * -0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 2.0), $MachinePrecision], 5e+28], N[(N[(N[(x * y), $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] + N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 2) < -2.0000000000000001e178

   1. Initial program 73.4%

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

      1. *-commutative 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*l* 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in x around 0 73.5%

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

      1. +-commutative 73.5%

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

      2. fma-def 73.5%

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

      3. associate-/l* 78.1%

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

      4. associate-/l* 98.9%

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

      5. associate-/r/ 83.3%

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

   6. Simplified 83.3%

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

      1. associate-*r* 83.2%

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

      2. associate-*r/ 83.2%

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

      3. associate-/r/ 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/l* 99.0%

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

   8. Applied egg-rr 99.0%

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

      1. fma-udef 99.0%

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

      2. div-inv 99.0%

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

      3. clear-num 99.1%

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

      4. div-inv 99.0%

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

      5. associate-/l/ 99.1%

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

      6. *-commutative 99.1%

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

      7. clear-num 99.0%

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

      8. associate-/l* 99.0%

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

      9. div-inv 98.9%

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

      10. metadata-eval 98.9%

          \[\leadsto 0.5 \cdot \left(x \cdot \frac{y}{a}\right) + t \cdot \frac{z}{a \cdot \color{blue}{-0.2222222222222222}} \]

   10. Applied egg-rr 98.9%

       \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right) + t \cdot \frac{z}{a \cdot -0.2222222222222222}} \]

   if -2.0000000000000001e178 < (*.f64 a 2) < 4.99999999999999957e28

   1. Initial program 98.2%

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

   if 4.99999999999999957e28 < (*.f64 a 2)

   1. Initial program 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

      3. associate-*l* 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in x around 0 75.0%

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

      1. +-commutative 75.0%

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

      2. fma-def 75.0%

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

      3. associate-/l* 86.5%

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

      4. associate-/l* 92.3%

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

      5. associate-/r/ 98.2%

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

   6. Simplified 98.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -2 \cdot 10^{+178}:\\ \;\;\;\;t \cdot \frac{z}{a \cdot -0.2222222222222222} + 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;a \cdot 2 \leq 5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{x}{\frac{a}{y}}, -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\right)\\ \end{array} \]

Alternative 3: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+251} \lor \neg \left(t_1 \leq 4 \cdot 10^{+275}\right):\\ \;\;\;\;t \cdot \frac{z}{a \cdot -0.2222222222222222} + 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (or (<= t_1 -5e+251) (not (<= t_1 4e+275)))
     (+ (* t (/ z (* a -0.2222222222222222))) (* 0.5 (* x (/ y a))))
     (/ (- (* x y) (* z (* t 9.0))) (* a 2.0)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -5e+251) || !(t_1 <= 4e+275)) {
		tmp = (t * (z / (a * -0.2222222222222222))) + (0.5 * (x * (y / a)));
	} else {
		tmp = ((x * y) - (z * (t * 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (t * (z * 9.0d0))
    if ((t_1 <= (-5d+251)) .or. (.not. (t_1 <= 4d+275))) then
        tmp = (t * (z / (a * (-0.2222222222222222d0)))) + (0.5d0 * (x * (y / a)))
    else
        tmp = ((x * y) - (z * (t * 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 t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -5e+251) || !(t_1 <= 4e+275)) {
		tmp = (t * (z / (a * -0.2222222222222222))) + (0.5 * (x * (y / a)));
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) - (t * (z * 9.0))
	tmp = 0
	if (t_1 <= -5e+251) or not (t_1 <= 4e+275):
		tmp = (t * (z / (a * -0.2222222222222222))) + (0.5 * (x * (y / a)))
	else:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(t * Float64(z * 9.0)))
	tmp = 0.0
	if ((t_1 <= -5e+251) || !(t_1 <= 4e+275))
		tmp = Float64(Float64(t * Float64(z / Float64(a * -0.2222222222222222))) + Float64(0.5 * Float64(x * Float64(y / a))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 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)
	t_1 = (x * y) - (t * (z * 9.0));
	tmp = 0.0;
	if ((t_1 <= -5e+251) || ~((t_1 <= 4e+275)))
		tmp = (t * (z / (a * -0.2222222222222222))) + (0.5 * (x * (y / a)));
	else
		tmp = ((x * y) - (z * (t * 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+251], N[Not[LessEqual[t$95$1, 4e+275]], $MachinePrecision]], N[(N[(t * N[(z / N[(a * -0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.0000000000000005e251 or 3.99999999999999984e275 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*l* 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in x around 0 68.0%

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

      1. +-commutative 68.0%

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

      2. fma-def 68.0%

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

      3. associate-/l* 79.9%

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

      4. associate-/l* 94.1%

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

      5. associate-/r/ 91.7%

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

   6. Simplified 91.7%

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

      1. associate-*r* 91.6%

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

      2. associate-*r/ 91.7%

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

      3. associate-/r/ 94.0%

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

      4. *-commutative 94.0%

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

      5. associate-/l* 94.0%

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

   8. Applied egg-rr 94.0%

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

      1. fma-udef 94.0%

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

      2. div-inv 93.9%

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

      3. clear-num 93.9%

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

      4. div-inv 93.9%

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

      5. associate-/l/ 93.9%

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

      6. *-commutative 93.9%

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

      7. clear-num 93.9%

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

      8. associate-/l* 93.9%

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

      9. div-inv 93.9%

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

      10. metadata-eval 93.9%

          \[\leadsto 0.5 \cdot \left(x \cdot \frac{y}{a}\right) + t \cdot \frac{z}{a \cdot \color{blue}{-0.2222222222222222}} \]

   10. Applied egg-rr 93.9%

       \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right) + t \cdot \frac{z}{a \cdot -0.2222222222222222}} \]

   if -5.0000000000000005e251 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 3.99999999999999984e275

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -5 \cdot 10^{+251} \lor \neg \left(x \cdot y - t \cdot \left(z \cdot 9\right) \leq 4 \cdot 10^{+275}\right):\\ \;\;\;\;t \cdot \frac{z}{a \cdot -0.2222222222222222} + 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 4: 92.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq 10^{+215}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

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 (* z 9.0)) 1e+215)
   (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
   (* -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 * (z * 9.0)) <= 1e+215) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} 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 * (z * 9.0d0)) <= 1d+215) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    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 * (z * 9.0)) <= 1e+215) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} 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 * (z * 9.0)) <= 1e+215:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	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 (Float64(t * Float64(z * 9.0)) <= 1e+215)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	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 * (z * 9.0)) <= 1e+215)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	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[N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision], 1e+215], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z 9) t) < 9.99999999999999907e214

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   if 9.99999999999999907e214 < (*.f64 (*.f64 z 9) t)

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*l* 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in x around 0 69.8%

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

      1. associate-/l* 96.4%

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

   6. Simplified 96.4%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq 10^{+215}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 5: 92.7% accurate, 0.8× speedup

Math

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

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 y) (- INFINITY))
   (* 0.5 (* y (/ x a)))
   (* (- (* x y) (* t (* z 9.0))) (/ 0.5 a))))

C

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

Java

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

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = ((x * y) - (t * (z * 9.0))) * (0.5 / a)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) * 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 ((x * y) <= -Inf)
		tmp = 0.5 * (y * (x / a));
	else
		tmp = ((x * y) - (t * (z * 9.0))) * (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[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 61.6%

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

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-*l* 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in x around 0 61.6%

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

      1. +-commutative 61.6%

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

      2. fma-def 61.6%

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

      3. associate-/l* 90.2%

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

      4. associate-/l* 99.8%

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

      5. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-*r/ 94.9%

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

   9. Simplified 94.9%

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

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

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. *-commutative 93.0%

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

      3. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

      1. div-sub 89.6%

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

      2. div-inv 89.5%

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

      3. *-commutative 89.5%

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

      4. associate-/r* 89.5%

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

      5. metadata-eval 89.5%

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

      6. div-inv 89.5%

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

      7. *-commutative 89.5%

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

      8. associate-/r* 89.5%

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

      9. metadata-eval 89.5%

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

   5. Applied egg-rr 89.5%

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

      1. distribute-rgt-out-- 92.8%

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

      2. associate-*r* 92.9%

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

      3. *-commutative 92.9%

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

   7. Applied egg-rr 92.9%

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

4. Final simplification 93.0%

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

Alternative 6: 73.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+49}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{t}}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+17)
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) 2e+49) (/ -4.5 (/ (/ a t) z)) (* 0.5 (* y (/ x a))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+17) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+49) {
		tmp = -4.5 / ((a / t) / z);
	} else {
		tmp = 0.5 * (y * (x / 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 ((x * y) <= (-2d+17)) then
        tmp = 0.5d0 * (x * (y / a))
    else if ((x * y) <= 2d+49) then
        tmp = (-4.5d0) / ((a / t) / z)
    else
        tmp = 0.5d0 * (y * (x / 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 ((x * y) <= -2e+17) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 2e+49) {
		tmp = -4.5 / ((a / t) / z);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+17:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= 2e+49:
		tmp = -4.5 / ((a / t) / z)
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+17)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= 2e+49)
		tmp = Float64(-4.5 / Float64(Float64(a / t) / z));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / 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 ((x * y) <= -2e+17)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= 2e+49)
		tmp = -4.5 / ((a / t) / z);
	else
		tmp = 0.5 * (y * (x / 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[LessEqual[N[(x * y), $MachinePrecision], -2e+17], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+49], N[(-4.5 / N[(N[(a / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e17

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

      2. *-commutative 87.4%

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

      3. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around inf 75.6%

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

      1. associate-/l* 83.8%

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

   6. Simplified 83.8%

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

      1. clear-num 83.8%

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

      2. associate-/r/ 83.8%

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

      3. clear-num 83.8%

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

   8. Applied egg-rr 83.8%

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

   if -2e17 < (*.f64 x y) < 1.99999999999999989e49

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. associate-*r/ 77.8%

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

      2. associate-*r* 77.8%

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

   6. Simplified 77.8%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 79.2%

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

      3. associate-*r/ 79.2%

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

      4. clear-num 79.3%

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

      5. un-div-inv 79.3%

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

   8. Applied egg-rr 79.3%

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

      1. associate-*l/ 79.4%

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

      2. associate-/l* 79.3%

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

   10. Applied egg-rr 79.3%

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

   if 1.99999999999999989e49 < (*.f64 x y)

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. *-commutative 87.5%

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

      3. associate-*l* 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in x around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. fma-def 79.9%

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

      3. associate-/l* 88.8%

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

      4. associate-/l* 90.4%

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

      5. associate-/r/ 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in x around inf 69.1%

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

      1. *-commutative 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-*r/ 74.3%

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

   9. Simplified 74.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+49}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{t}}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 7: 68.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+34}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e-158)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 2.25e+34) (* 0.5 (* x (/ y a))) (* -4.5 (* z (/ t a))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e-158) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 2.25e+34) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (z * (t / 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 <= (-3.1d-158)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 2.25d+34) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * (z * (t / 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 <= -3.1e-158) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 2.25e+34) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e-158:
		tmp = -4.5 * (t / (a / z))
	elif t <= 2.25e+34:
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e-158)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 2.25e+34)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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 <= -3.1e-158)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 2.25e+34)
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * (z * (t / 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[LessEqual[t, -3.1e-158], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+34], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.10000000000000018e-158

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in x around 0 58.1%

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

      1. associate-/l* 65.7%

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

   6. Simplified 65.7%

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

   if -3.10000000000000018e-158 < t < 2.25e34

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. *-commutative 93.8%

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

      3. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in x around inf 70.6%

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

      1. associate-/l* 75.1%

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

   6. Simplified 75.1%

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

      1. clear-num 75.2%

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

      2. associate-/r/ 74.5%

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

      3. clear-num 74.6%

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

   8. Applied egg-rr 74.6%

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

   if 2.25e34 < t

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 64.3%

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

      1. associate-/l* 60.9%

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

      2. associate-/r/ 77.7%

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

   6. Simplified 77.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+34}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 8: 68.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+33}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e-158)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 7.4e+33) (* 0.5 (/ x (/ a y))) (* -4.5 (* z (/ t a))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e-158) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 7.4e+33) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = -4.5 * (z * (t / 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 <= (-3.1d-158)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 7.4d+33) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = (-4.5d0) * (z * (t / 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 <= -3.1e-158) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 7.4e+33) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e-158:
		tmp = -4.5 * (t / (a / z))
	elif t <= 7.4e+33:
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e-158)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 7.4e+33)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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 <= -3.1e-158)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 7.4e+33)
		tmp = 0.5 * (x / (a / y));
	else
		tmp = -4.5 * (z * (t / 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[LessEqual[t, -3.1e-158], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.4e+33], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.10000000000000018e-158

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in x around 0 58.1%

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

      1. associate-/l* 65.7%

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

   6. Simplified 65.7%

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

   if -3.10000000000000018e-158 < t < 7.3999999999999997e33

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. *-commutative 93.8%

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

      3. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in x around inf 70.6%

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

      1. associate-/l* 75.1%

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

   6. Simplified 75.1%

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

   if 7.3999999999999997e33 < t

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 64.3%

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

      1. associate-/l* 60.9%

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

      2. associate-/r/ 77.7%

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

   6. Simplified 77.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+33}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 9: 67.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-194}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e-194)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 1.7e+34) (* y (* x (/ 0.5 a))) (* -4.5 (* z (/ t a))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e-194) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 1.7e+34) {
		tmp = y * (x * (0.5 / a));
	} else {
		tmp = -4.5 * (z * (t / 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 <= (-8d-194)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 1.7d+34) then
        tmp = y * (x * (0.5d0 / a))
    else
        tmp = (-4.5d0) * (z * (t / 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 <= -8e-194) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 1.7e+34) {
		tmp = y * (x * (0.5 / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e-194:
		tmp = -4.5 * (t / (a / z))
	elif t <= 1.7e+34:
		tmp = y * (x * (0.5 / a))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e-194)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 1.7e+34)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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 <= -8e-194)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 1.7e+34)
		tmp = y * (x * (0.5 / a));
	else
		tmp = -4.5 * (z * (t / 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[LessEqual[t, -8e-194], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+34], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000014e-194

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around 0 57.1%

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

      1. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   if -8.00000000000000014e-194 < t < 1.7e34

   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. *-commutative 93.3%

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

      2. *-commutative 93.3%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. fma-def 92.1%

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

      3. associate-/l* 96.9%

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

      4. associate-/l* 90.5%

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

      5. associate-/r/ 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in x around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-*l/ 71.6%

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

      3. associate-*r/ 71.6%

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

      4. *-commutative 71.6%

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

      5. associate-*l* 74.8%

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

   9. Simplified 74.8%

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

   if 1.7e34 < t

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 64.3%

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

      1. associate-/l* 60.9%

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

      2. associate-/r/ 77.7%

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

   6. Simplified 77.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-194}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 10: 67.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-194}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+34}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e-194)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 1.35e+34) (* 0.5 (* y (/ x a))) (* -4.5 (* z (/ t a))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e-194) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 1.35e+34) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * (z * (t / 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 <= (-8d-194)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 1.35d+34) then
        tmp = 0.5d0 * (y * (x / a))
    else
        tmp = (-4.5d0) * (z * (t / 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 <= -8e-194) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 1.35e+34) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e-194:
		tmp = -4.5 * (t / (a / z))
	elif t <= 1.35e+34:
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e-194)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 1.35e+34)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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 <= -8e-194)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 1.35e+34)
		tmp = 0.5 * (y * (x / a));
	else
		tmp = -4.5 * (z * (t / 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[LessEqual[t, -8e-194], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+34], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000014e-194

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around 0 57.1%

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

      1. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   if -8.00000000000000014e-194 < t < 1.35e34

   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. *-commutative 93.3%

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

      2. *-commutative 93.3%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. fma-def 92.1%

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

      3. associate-/l* 96.9%

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

      4. associate-/l* 90.5%

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

      5. associate-/r/ 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in x around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*r/ 74.8%

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

   9. Simplified 74.8%

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

   if 1.35e34 < t

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 64.3%

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

      1. associate-/l* 60.9%

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

      2. associate-/r/ 77.7%

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

   6. Simplified 77.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-194}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+34}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 11: 67.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-194}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}}\\ \end{array} \end{array} \]

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 -8e-194)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 9.5e+33) (* 0.5 (* y (/ x a))) (* z (/ -4.5 (/ a t))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e-194) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 9.5e+33) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = z * (-4.5 / (a / t));
	}
	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 <= (-8d-194)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 9.5d+33) then
        tmp = 0.5d0 * (y * (x / a))
    else
        tmp = z * ((-4.5d0) / (a / t))
    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 <= -8e-194) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 9.5e+33) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = z * (-4.5 / (a / t));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e-194:
		tmp = -4.5 * (t / (a / z))
	elif t <= 9.5e+33:
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = z * (-4.5 / (a / t))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e-194)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 9.5e+33)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(z * Float64(-4.5 / Float64(a / t)));
	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 <= -8e-194)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 9.5e+33)
		tmp = 0.5 * (y * (x / a));
	else
		tmp = z * (-4.5 / (a / t));
	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, -8e-194], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+33], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(-4.5 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000014e-194

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around 0 57.1%

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

      1. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   if -8.00000000000000014e-194 < t < 9.5000000000000003e33

   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. *-commutative 93.3%

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

      2. *-commutative 93.3%

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

      3. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. fma-def 92.1%

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

      3. associate-/l* 96.9%

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

      4. associate-/l* 90.5%

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

      5. associate-/r/ 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in x around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*r/ 74.8%

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

   9. Simplified 74.8%

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

   if 9.5000000000000003e33 < t

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 64.3%

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

      1. associate-*r/ 64.3%

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

      2. associate-*r* 64.3%

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

   6. Simplified 64.3%

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

      1. associate-/l* 60.9%

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

      2. associate-/r/ 77.6%

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

      3. associate-*r/ 77.6%

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

      4. clear-num 77.6%

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

      5. un-div-inv 77.6%

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

   8. Applied egg-rr 77.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-194}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}}\\ \end{array} \]

Alternative 12: 50.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{+69}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.56e+69) (* -4.5 (/ t (/ a z))) (* -4.5 (* z (/ t a)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.56e+69) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * (z * (t / 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 (x <= (-1.56d+69)) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (-4.5d0) * (z * (t / 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 (x <= -1.56e+69) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.56e+69:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.56e+69)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / 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 (x <= -1.56e+69)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = -4.5 * (z * (t / 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[LessEqual[x, -1.56e+69], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.56000000000000007e69

   1. Initial program 92.2%

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

      1. *-commutative 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around 0 31.2%

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

      1. associate-/l* 31.3%

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

   6. Simplified 31.3%

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

   if -1.56000000000000007e69 < x

   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. *-commutative 90.3%

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

      2. *-commutative 90.3%

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

      3. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around 0 56.6%

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

      1. associate-/l* 57.9%

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

      2. associate-/r/ 61.0%

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

   6. Simplified 61.0%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{+69}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 13: 51.1% accurate, 1.9× speedup

Math

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

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 (* z (/ t a))))

C

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

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) * (z * (t / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 90.6%

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

   1. *-commutative 90.6%

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

   2. *-commutative 90.6%

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

   3. associate-*l* 90.6%

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

3. Simplified 90.6%

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

4. Taylor expanded in x around 0 51.9%

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

   1. associate-/l* 53.0%

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

   2. associate-/r/ 56.3%

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

6. Simplified 56.3%

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

7. Final simplification 56.3%

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

Developer target: 93.3% 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 2023314 
(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)))