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

Percentage Accurate: 91.3% → 96.6%

Time: 11.3s

Alternatives: 9

Speedup: 0.6×

• 28.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, \frac{y}{2} \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+200}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{a} \cdot 0.5, \frac{t}{\frac{a}{z \cdot -4.5}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (fma -4.5 (* z (/ t a)) (* (/ y 2.0) (/ x a)))
     (if (<= t_1 5e+200)
       (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
       (fma x (* (/ y a) 0.5) (/ t (/ a (* z -4.5))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(-4.5, (z * (t / a)), ((y / 2.0) * (x / a)));
	} else if (t_1 <= 5e+200) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = fma(x, ((y / a) * 0.5), (t / (a / (z * -4.5))));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(-4.5, Float64(z * Float64(t / a)), Float64(Float64(y / 2.0) * Float64(x / a)));
	elseif (t_1 <= 5e+200)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = fma(x, Float64(Float64(y / a) * 0.5), Float64(t / Float64(a / Float64(z * -4.5))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+200], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / a), $MachinePrecision] * 0.5), $MachinePrecision] + N[(t / N[(a / N[(z * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.6%

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

      1. associate-*l* 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. fma-def 61.5%

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

      2. associate-/l* 79.1%

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

      3. associate-/r/ 79.1%

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

      4. associate-*r/ 79.1%

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

      5. *-commutative 79.1%

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

      6. associate-*r* 79.1%

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

   7. Simplified 79.1%

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

      1. div-inv 79.1%

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

      2. associate-*l* 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-*l* 79.1%

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

      5. metadata-eval 79.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, \color{blue}{\frac{1}{2}} \cdot \left(\left(x \cdot y\right) \cdot \frac{1}{a}\right)\right) \]

      6. div-inv 79.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, \frac{1}{2} \cdot \color{blue}{\frac{x \cdot y}{a}}\right) \]

      7. times-frac 79.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, \color{blue}{\frac{1 \cdot \left(x \cdot y\right)}{2 \cdot a}}\right) \]

      8. *-un-lft-identity 79.1%

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

      9. *-commutative 79.1%

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

      10. times-frac 93.6%

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

   9. Applied egg-rr 93.6%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5.00000000000000019e200

   1. Initial program 99.5%

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

      1. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   if 5.00000000000000019e200 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 76.1%

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

      1. associate-*l* 76.0%

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

   3. Simplified 76.0%

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

      1. add-sqr-sqrt 35.5%

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

      2. sqrt-unprod 45.9%

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

      3. swap-sqr 45.9%

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

      4. metadata-eval 45.9%

         \[\leadsto \frac{x \cdot y - z \cdot \sqrt{\color{blue}{81} \cdot \left(t \cdot t\right)}}{a \cdot 2} \]

      5. metadata-eval 45.9%

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

      6. swap-sqr 45.9%

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

      7. *-commutative 45.9%

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

      8. *-commutative 45.9%

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

      9. sqrt-unprod 15.2%

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

      10. add-sqr-sqrt 28.1%

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

      11. add-cube-cbrt 28.1%

          \[\leadsto \frac{x \cdot y - \color{blue}{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)} \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}\right) \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}}}{a \cdot 2} \]

      12. pow3 28.1%

          \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)}\right)}^{3}}}{a \cdot 2} \]

   6. Applied egg-rr 76.0%

      \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{9 \cdot \left(z \cdot t\right)}\right)}^{3}}}{a \cdot 2} \]

   7. Taylor expanded in x around 0 76.0%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left({1}^{0.3333333333333333} \cdot \left(t \cdot z\right)\right) + x \cdot y}}{a \cdot 2} \]
   8. Step-by-step derivation

      1. fma-def 76.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, {1}^{0.3333333333333333} \cdot \left(t \cdot z\right), x \cdot y\right)}}{a \cdot 2} \]

      2. pow-base-1 76.0%

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

      3. *-commutative 76.0%

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

      4. *-lft-identity 76.0%

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

      5. fma-def 76.0%

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

      6. associate-*r* 76.1%

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

      7. metadata-eval 76.1%

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

      8. distribute-lft-neg-in 76.1%

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

      9. *-commutative 76.1%

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

      10. fma-def 78.6%

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

      11. distribute-lft-neg-in 78.6%

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

      12. metadata-eval 78.6%

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

      13. *-commutative 78.6%

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

   9. Simplified 78.6%

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

   10. Taylor expanded in t around 0 68.6%

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

   12. Simplified 87.3%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, \frac{y}{2} \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+200}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{a} \cdot 0.5, \frac{t}{\frac{a}{z \cdot -4.5}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+167}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \frac{t \cdot -9}{2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* -4.5 (* t (/ z a)))
     (if (<= t_1 2e+167)
       (/ (fma x y (* z (* t -9.0))) (* a 2.0))
       (* (/ z a) (/ (* t -9.0) 2.0))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -4.5 * (t * (z / a));
	} else if (t_1 <= 2e+167) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = (z / a) * ((t * -9.0) / 2.0);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (t_1 <= 2e+167)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(z / a) * Float64(Float64(t * -9.0) / 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+167], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * N[(N[(t * -9.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 62.8%

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

      1. associate-*l* 62.8%

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

   3. Simplified 62.8%

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

      1. add-sqr-sqrt 28.4%

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

      2. sqrt-unprod 34.0%

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

      3. swap-sqr 34.0%

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

      4. metadata-eval 34.0%

         \[\leadsto \frac{x \cdot y - z \cdot \sqrt{\color{blue}{81} \cdot \left(t \cdot t\right)}}{a \cdot 2} \]

      5. metadata-eval 34.0%

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

      6. swap-sqr 34.0%

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

      7. *-commutative 34.0%

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

      8. *-commutative 34.0%

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

      9. sqrt-unprod 5.6%

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

      10. add-sqr-sqrt 5.6%

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

      11. add-cube-cbrt 5.6%

          \[\leadsto \frac{x \cdot y - \color{blue}{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)} \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}\right) \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}}}{a \cdot 2} \]

      12. pow3 5.6%

          \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)}\right)}^{3}}}{a \cdot 2} \]

   6. Applied egg-rr 62.8%

      \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{9 \cdot \left(z \cdot t\right)}\right)}^{3}}}{a \cdot 2} \]

   7. Taylor expanded in x around 0 68.4%

      \[\leadsto \color{blue}{-4.5 \cdot \left({1}^{0.3333333333333333} \cdot \frac{t \cdot z}{a}\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 68.4%

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

      2. associate-*r* 68.4%

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

      3. metadata-eval 68.4%

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

      4. *-commutative 68.4%

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

      5. associate-*l/ 94.4%

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

   9. Simplified 94.4%

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

   if -inf.0 < (*.f64 (*.f64 z 9) t) < 2.0000000000000001e167

   1. Initial program 95.5%

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

      1. div-sub 95.0%

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

      2. *-commutative 95.0%

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

      3. div-sub 95.5%

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

      4. *-commutative 95.5%

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

      5. cancel-sign-sub-inv 95.5%

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

      6. fma-def 95.5%

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

      7. distribute-lft-neg-in 95.5%

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

      8. associate-*l* 95.5%

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

      9. distribute-rgt-neg-in 95.5%

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

      10. *-commutative 95.5%

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

      11. distribute-rgt-neg-in 95.5%

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

      12. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   if 2.0000000000000001e167 < (*.f64 (*.f64 z 9) t)

   1. Initial program 82.2%

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

      1. associate-*l* 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in x around 0 82.2%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

      3. times-frac 99.9%

         \[\leadsto \color{blue}{\frac{-9 \cdot t}{2} \cdot \frac{z}{a}} \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{-9 \cdot t}{2} \cdot \frac{z}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+167}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \frac{t \cdot -9}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], (-Infinity)], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + 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)) < -inf.0

   1. Initial program 64.6%

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

      1. associate-*l* 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. fma-def 61.5%

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

      2. associate-/l* 79.1%

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

      3. associate-/r/ 79.1%

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

      4. associate-*r/ 79.1%

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

      5. *-commutative 79.1%

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

      6. associate-*r* 79.1%

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

   7. Simplified 79.1%

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

      1. div-inv 79.1%

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

      2. associate-*l* 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-*l* 79.1%

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

      5. metadata-eval 79.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, \color{blue}{\frac{1}{2}} \cdot \left(\left(x \cdot y\right) \cdot \frac{1}{a}\right)\right) \]

      6. div-inv 79.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, \frac{1}{2} \cdot \color{blue}{\frac{x \cdot y}{a}}\right) \]

      7. times-frac 79.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, \color{blue}{\frac{1 \cdot \left(x \cdot y\right)}{2 \cdot a}}\right) \]

      8. *-un-lft-identity 79.1%

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

      9. *-commutative 79.1%

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

      10. times-frac 93.6%

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

   9. Applied egg-rr 93.6%

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

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

   1. Initial program 95.3%

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

      1. div-sub 93.1%

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

      2. *-commutative 93.1%

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

      3. div-sub 95.3%

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

      4. *-commutative 95.3%

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

      5. cancel-sign-sub-inv 95.3%

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

      6. fma-def 95.8%

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

      7. distribute-lft-neg-in 95.8%

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

      8. associate-*l* 95.8%

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

      9. distribute-rgt-neg-in 95.8%

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

      10. *-commutative 95.8%

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

      11. distribute-rgt-neg-in 95.8%

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

      12. metadata-eval 95.8%

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

   3. Simplified 95.8%

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

4. Final simplification 95.6%

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

Alternative 4: 94.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+167}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \frac{t \cdot -9}{2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* -4.5 (* t (/ z a)))
     (if (<= t_1 2e+167)
       (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
       (* (/ z a) (/ (* t -9.0) 2.0))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -4.5 * (t * (z / a));
	} else if (t_1 <= 2e+167) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = (z / a) * ((t * -9.0) / 2.0);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -4.5 * (t * (z / a));
	} else if (t_1 <= 2e+167) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = (z / a) * ((t * -9.0) / 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -4.5 * (t * (z / a))
	elif t_1 <= 2e+167:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = (z / a) * ((t * -9.0) / 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (t_1 <= 2e+167)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(z / a) * Float64(Float64(t * -9.0) / 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -4.5 * (t * (z / a));
	elseif (t_1 <= 2e+167)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = (z / a) * ((t * -9.0) / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+167], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * N[(N[(t * -9.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 62.8%

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

      1. associate-*l* 62.8%

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

   3. Simplified 62.8%

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

      1. add-sqr-sqrt 28.4%

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

      2. sqrt-unprod 34.0%

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

      3. swap-sqr 34.0%

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

      4. metadata-eval 34.0%

         \[\leadsto \frac{x \cdot y - z \cdot \sqrt{\color{blue}{81} \cdot \left(t \cdot t\right)}}{a \cdot 2} \]

      5. metadata-eval 34.0%

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

      6. swap-sqr 34.0%

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

      7. *-commutative 34.0%

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

      8. *-commutative 34.0%

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

      9. sqrt-unprod 5.6%

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

      10. add-sqr-sqrt 5.6%

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

      11. add-cube-cbrt 5.6%

          \[\leadsto \frac{x \cdot y - \color{blue}{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)} \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}\right) \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}}}{a \cdot 2} \]

      12. pow3 5.6%

          \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)}\right)}^{3}}}{a \cdot 2} \]

   6. Applied egg-rr 62.8%

      \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{9 \cdot \left(z \cdot t\right)}\right)}^{3}}}{a \cdot 2} \]

   7. Taylor expanded in x around 0 68.4%

      \[\leadsto \color{blue}{-4.5 \cdot \left({1}^{0.3333333333333333} \cdot \frac{t \cdot z}{a}\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 68.4%

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

      2. associate-*r* 68.4%

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

      3. metadata-eval 68.4%

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

      4. *-commutative 68.4%

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

      5. associate-*l/ 94.4%

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

   9. Simplified 94.4%

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

   if -inf.0 < (*.f64 (*.f64 z 9) t) < 2.0000000000000001e167

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   if 2.0000000000000001e167 < (*.f64 (*.f64 z 9) t)

   1. Initial program 82.2%

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

      1. associate-*l* 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in x around 0 82.2%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

      3. times-frac 99.9%

         \[\leadsto \color{blue}{\frac{-9 \cdot t}{2} \cdot \frac{z}{a}} \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{-9 \cdot t}{2} \cdot \frac{z}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+167}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \frac{t \cdot -9}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y * N[(N[(x / a), $MachinePrecision] * 0.5), $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 52.2%

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

      1. associate-*l* 52.2%

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

   3. Simplified 52.2%

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

      1. add-sqr-sqrt 25.3%

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

      2. sqrt-unprod 52.2%

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

      3. swap-sqr 52.2%

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

      4. metadata-eval 52.2%

         \[\leadsto \frac{x \cdot y - z \cdot \sqrt{\color{blue}{81} \cdot \left(t \cdot t\right)}}{a \cdot 2} \]

      5. metadata-eval 52.2%

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

      6. swap-sqr 52.2%

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

      7. *-commutative 52.2%

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

      8. *-commutative 52.2%

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

      9. sqrt-unprod 33.2%

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

      10. add-sqr-sqrt 52.2%

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

      11. add-cube-cbrt 52.2%

          \[\leadsto \frac{x \cdot y - \color{blue}{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)} \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}\right) \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}}}{a \cdot 2} \]

      12. pow3 52.2%

          \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)}\right)}^{3}}}{a \cdot 2} \]

   6. Applied egg-rr 52.2%

      \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{9 \cdot \left(z \cdot t\right)}\right)}^{3}}}{a \cdot 2} \]

   7. Taylor expanded in x around inf 58.5%

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

      1. associate-*r/ 58.5%

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

      2. *-commutative 58.5%

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

      3. associate-*r* 58.5%

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

      4. *-rgt-identity 58.5%

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

      5. associate-*r/ 58.5%

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

      6. *-commutative 58.5%

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

      7. associate-*r* 93.6%

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

      8. associate-*l* 93.6%

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

      9. associate-*r/ 93.6%

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

      10. *-rgt-identity 93.6%

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

   9. Simplified 93.6%

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

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

   1. Initial program 94.1%

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

      1. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

      1. add-sqr-sqrt 50.3%

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

      2. sqrt-unprod 58.6%

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

      3. swap-sqr 58.6%

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

      4. metadata-eval 58.6%

         \[\leadsto \frac{x \cdot y - z \cdot \sqrt{\color{blue}{81} \cdot \left(t \cdot t\right)}}{a \cdot 2} \]

      5. metadata-eval 58.6%

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

      6. swap-sqr 58.6%

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

      7. *-commutative 58.6%

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

      8. *-commutative 58.6%

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

      9. sqrt-unprod 19.9%

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

      10. add-sqr-sqrt 44.8%

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

      11. add-cube-cbrt 44.8%

          \[\leadsto \frac{x \cdot y - \color{blue}{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)} \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}\right) \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}}}{a \cdot 2} \]

      12. pow3 44.8%

          \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)}\right)}^{3}}}{a \cdot 2} \]

   6. Applied egg-rr 93.7%

      \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{9 \cdot \left(z \cdot t\right)}\right)}^{3}}}{a \cdot 2} \]

   7. Taylor expanded in x around 0 94.2%

      \[\leadsto \frac{\color{blue}{-9 \cdot \left({1}^{0.3333333333333333} \cdot \left(t \cdot z\right)\right) + x \cdot y}}{a \cdot 2} \]
   8. Step-by-step derivation

      1. fma-def 94.2%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9, {1}^{0.3333333333333333} \cdot \left(t \cdot z\right), x \cdot y\right)}}{a \cdot 2} \]

      2. pow-base-1 94.2%

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

      3. *-commutative 94.2%

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

      4. *-lft-identity 94.2%

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

      5. fma-def 94.2%

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

      6. associate-*r* 94.1%

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

      7. metadata-eval 94.1%

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

      8. distribute-lft-neg-in 94.1%

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

      9. *-commutative 94.1%

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

      10. fma-def 94.1%

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

      11. distribute-lft-neg-in 94.1%

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

      12. metadata-eval 94.1%

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

      13. *-commutative 94.1%

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

   9. Simplified 94.1%

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

       1. div-inv 94.1%

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

       2. *-commutative 94.1%

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

       3. associate-/r* 94.1%

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

       4. metadata-eval 94.1%

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

   11. Applied egg-rr 94.1%

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

       1. fma-udef 94.1%

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

       2. +-commutative 94.1%

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

   13. Applied egg-rr 94.1%

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

4. Final simplification 94.1%

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

Alternative 6: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+54}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{a}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e-193)
   (* -4.5 (* z (/ t a)))
   (if (<= t 2.4e+54) (* 0.5 (/ 1.0 (/ a (* x y)))) (* -4.5 (/ z (/ a t))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-193) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 2.4e+54) {
		tmp = 0.5 * (1.0 / (a / (x * y)));
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.2d-193)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t <= 2.4d+54) then
        tmp = 0.5d0 * (1.0d0 / (a / (x * y)))
    else
        tmp = (-4.5d0) * (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-193) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 2.4e+54) {
		tmp = 0.5 * (1.0 / (a / (x * y)));
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e-193:
		tmp = -4.5 * (z * (t / a))
	elif t <= 2.4e+54:
		tmp = 0.5 * (1.0 / (a / (x * y)))
	else:
		tmp = -4.5 * (z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e-193)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t <= 2.4e+54)
		tmp = Float64(0.5 * Float64(1.0 / Float64(a / Float64(x * y))));
	else
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e-193)
		tmp = -4.5 * (z * (t / a));
	elseif (t <= 2.4e+54)
		tmp = 0.5 * (1.0 / (a / (x * y)));
	else
		tmp = -4.5 * (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e-193], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+54], N[(0.5 * N[(1.0 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e-193

   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. 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. Add Preprocessing

   5. Taylor expanded in x around 0 61.5%

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

      1. associate-/l* 62.1%

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

      2. associate-/r/ 61.8%

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

   7. Simplified 61.8%

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

   if -1.2e-193 < t < 2.39999999999999998e54

   1. Initial program 96.8%

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

      1. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 71.3%

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

      1. associate-*r/ 64.6%

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

   7. Simplified 64.6%

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

      1. associate-*r/ 71.3%

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

      2. clear-num 71.3%

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

   9. Applied egg-rr 71.3%

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

   if 2.39999999999999998e54 < t

   1. Initial program 89.5%

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

      1. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in x around 0 76.2%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 79.8%

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

   7. Simplified 79.8%

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

      1. *-commutative 79.8%

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

      2. clear-num 79.6%

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

      3. un-div-inv 82.0%

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

   9. Applied egg-rr 82.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+54}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{a}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e-193)
   (* -4.5 (* z (/ t a)))
   (if (<= t 1.3e+27) (* 0.5 (* x (/ y a))) (* -4.5 (/ z (/ a t))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-193) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 1.3e+27) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.2d-193)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t <= 1.3d+27) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-193) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 1.3e+27) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e-193:
		tmp = -4.5 * (z * (t / a))
	elif t <= 1.3e+27:
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * (z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e-193)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t <= 1.3e+27)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e-193)
		tmp = -4.5 * (z * (t / a));
	elseif (t <= 1.3e+27)
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e-193], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+27], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e-193

   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. 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. Add Preprocessing

   5. Taylor expanded in x around 0 61.5%

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

      1. associate-/l* 62.1%

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

      2. associate-/r/ 61.8%

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

   7. Simplified 61.8%

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

   if -1.2e-193 < t < 1.30000000000000004e27

   1. Initial program 96.6%

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

      1. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around inf 73.1%

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

      1. associate-*r/ 66.2%

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

   7. Simplified 66.2%

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

   if 1.30000000000000004e27 < t

   1. Initial program 90.2%

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

      1. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in x around 0 76.1%

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

      1. associate-/l* 75.7%

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

      2. associate-/r/ 79.4%

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

   7. Simplified 79.4%

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

      1. *-commutative 79.4%

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

      2. clear-num 79.3%

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

      3. un-div-inv 81.6%

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

   9. Applied egg-rr 81.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e-193)
   (* -4.5 (* z (/ t a)))
   (if (<= t 6.5e+54) (/ (* x (* y 0.5)) a) (* -4.5 (/ z (/ a t))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-193) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 6.5e+54) {
		tmp = (x * (y * 0.5)) / a;
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.2d-193)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (t <= 6.5d+54) then
        tmp = (x * (y * 0.5d0)) / a
    else
        tmp = (-4.5d0) * (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-193) {
		tmp = -4.5 * (z * (t / a));
	} else if (t <= 6.5e+54) {
		tmp = (x * (y * 0.5)) / a;
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e-193:
		tmp = -4.5 * (z * (t / a))
	elif t <= 6.5e+54:
		tmp = (x * (y * 0.5)) / a
	else:
		tmp = -4.5 * (z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e-193)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t <= 6.5e+54)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	else
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e-193)
		tmp = -4.5 * (z * (t / a));
	elseif (t <= 6.5e+54)
		tmp = (x * (y * 0.5)) / a;
	else
		tmp = -4.5 * (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e-193], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+54], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e-193

   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. 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. Add Preprocessing

   5. Taylor expanded in x around 0 61.5%

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

      1. associate-/l* 62.1%

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

      2. associate-/r/ 61.8%

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

   7. Simplified 61.8%

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

   if -1.2e-193 < t < 6.5e54

   1. Initial program 96.8%

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

      1. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 71.3%

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

      1. associate-*r/ 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*r* 71.3%

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

   7. Simplified 71.3%

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

   if 6.5e54 < t

   1. Initial program 89.5%

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

      1. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in x around 0 76.2%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 79.8%

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

   7. Simplified 79.8%

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

      1. *-commutative 79.8%

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

      2. clear-num 79.6%

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

      3. un-div-inv 82.0%

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

   9. Applied egg-rr 82.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-193}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.6% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (-4.5d0) * (z * (t / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. associate-*l* 91.6%

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

3. Simplified 91.6%

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

5. Taylor expanded in x around 0 55.1%

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

   1. associate-/l* 54.1%

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

   2. associate-/r/ 55.3%

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

7. Simplified 55.3%

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

8. Final simplification 55.3%

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

Developer target: 93.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024026 
(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)))