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

Percentage Accurate: 91.2% → 97.4%

Time: 8.4s

Alternatives: 10

Speedup: 0.4×

• 28.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}} + x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+264)))
     (+ (* z (/ -4.5 (/ a t))) (* x (* 0.5 (/ y a))))
     (/ t_1 (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+264)) {
		tmp = (z * (-4.5 / (a / t))) + (x * (0.5 * (y / a)));
	} else {
		tmp = t_1 / (a * 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 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+264)) {
		tmp = (z * (-4.5 / (a / t))) + (x * (0.5 * (y / a)));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+264):
		tmp = (z * (-4.5 / (a / t))) + (x * (0.5 * (y / a)))
	else:
		tmp = t_1 / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+264))
		tmp = Float64(Float64(z * Float64(-4.5 / Float64(a / t))) + Float64(x * Float64(0.5 * Float64(y / a))));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+264)))
		tmp = (z * (-4.5 / (a / t))) + (x * (0.5 * (y / a)));
	else
		tmp = t_1 / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+264]], $MachinePrecision]], N[(N[(z * N[(-4.5 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0 or 2.00000000000000009e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 74.5%

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

      1. associate-*l* 74.5%

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

   3. Simplified 74.5%

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

      1. div-sub 73.1%

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

      2. sub-neg 73.1%

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

      3. *-commutative 73.1%

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

      4. times-frac 79.5%

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

      5. div-inv 79.5%

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

      6. *-commutative 79.5%

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

      7. associate-*l* 79.5%

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

      8. *-commutative 79.5%

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

      9. associate-/r* 79.5%

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

      10. metadata-eval 79.5%

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

   6. Applied egg-rr 79.5%

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

      1. +-commutative 79.5%

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

      2. distribute-rgt-neg-in 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*l* 79.5%

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

      5. fma-def 79.5%

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

      6. distribute-neg-frac 79.5%

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

      7. metadata-eval 79.5%

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

      8. metadata-eval 79.5%

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

      9. associate-*r/ 79.5%

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

      10. metadata-eval 79.5%

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

      11. metadata-eval 79.5%

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

   8. Simplified 79.5%

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

      1. fma-udef 79.5%

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

      2. associate-*r/ 79.5%

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

      3. associate-*l/ 79.5%

         \[\leadsto \color{blue}{\frac{t \cdot z}{a} \cdot -4.5} + \frac{x}{2} \cdot \frac{y}{a} \]

      4. associate-*l/ 95.5%

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

      5. *-commutative 95.5%

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

      6. associate-*l* 95.6%

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

      7. *-commutative 95.6%

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

      8. clear-num 95.5%

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

      9. un-div-inv 95.6%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5}{\frac{a}{t}}} + \frac{x}{2} \cdot \frac{y}{a} \]

      10. div-inv 95.6%

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

      11. metadata-eval 95.6%

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

      12. associate-*l* 95.6%

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

   10. Applied egg-rr 95.6%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 2.00000000000000009e264

   1. Initial program 99.2%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}} + x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+275}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+198}:\\ \;\;\;\;\frac{x \cdot y - t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{t}}{z}}\\ \end{array} \end{array} \]

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 -5e+275)
     (* (* z -4.5) (/ t a))
     (if (<= t_1 2e+198)
       (/ (- (* x y) t_1) (* a 2.0))
       (/ -4.5 (/ (/ a t) z))))))

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 <= -5e+275) {
		tmp = (z * -4.5) * (t / a);
	} else if (t_1 <= 2e+198) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = -4.5 / ((a / t) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-5d+275)) then
        tmp = (z * (-4.5d0)) * (t / a)
    else if (t_1 <= 2d+198) then
        tmp = ((x * y) - t_1) / (a * 2.0d0)
    else
        tmp = (-4.5d0) / ((a / t) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+275) {
		tmp = (z * -4.5) * (t / a);
	} else if (t_1 <= 2e+198) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = -4.5 / ((a / t) / z);
	}
	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 <= -5e+275:
		tmp = (z * -4.5) * (t / a)
	elif t_1 <= 2e+198:
		tmp = ((x * y) - t_1) / (a * 2.0)
	else:
		tmp = -4.5 / ((a / t) / z)
	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 <= -5e+275)
		tmp = Float64(Float64(z * -4.5) * Float64(t / a));
	elseif (t_1 <= 2e+198)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	else
		tmp = Float64(-4.5 / Float64(Float64(a / t) / z));
	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 <= -5e+275)
		tmp = (z * -4.5) * (t / a);
	elseif (t_1 <= 2e+198)
		tmp = ((x * y) - t_1) / (a * 2.0);
	else
		tmp = -4.5 / ((a / t) / z);
	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, -5e+275], N[(N[(z * -4.5), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+198], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 / N[(N[(a / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z 9) t) < -5.0000000000000003e275

   1. Initial program 63.4%

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

      1. associate-*l* 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in x around 0 63.4%

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

      1. associate-*l/ 94.5%

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

   7. Simplified 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-/r/ 94.3%

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

      3. associate-*l/ 94.5%

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

   9. Applied egg-rr 94.5%

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

       1. associate-/r/ 94.7%

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

       2. *-commutative 94.7%

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

       3. *-un-lft-identity 94.7%

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

       4. times-frac 94.7%

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

       5. metadata-eval 94.7%

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

       6. clear-num 94.3%

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

       7. div-inv 94.6%

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

       8. *-commutative 94.6%

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

       9. associate-*r/ 94.7%

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

       10. div-inv 94.4%

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

       11. clear-num 94.6%

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

   11. Applied egg-rr 94.6%

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

   if -5.0000000000000003e275 < (*.f64 (*.f64 z 9) t) < 2.00000000000000004e198

   1. Initial program 96.0%

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

   if 2.00000000000000004e198 < (*.f64 (*.f64 z 9) t)

   1. Initial program 87.6%

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

      1. associate-*l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 87.5%

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

      1. associate-*l/ 99.8%

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

   7. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 97.4%

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

      3. un-div-inv 97.3%

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

   9. Applied egg-rr 97.3%

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

       1. clear-num 97.4%

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

       2. un-div-inv 97.4%

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

   11. Applied egg-rr 97.4%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+275}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+198}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{t}}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+56} \lor \neg \left(z \leq 2.3 \cdot 10^{-123}\right):\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+56) (not (<= z 2.3e-123)))
   (* -4.5 (/ z (/ a t)))
   (* 0.5 (/ x (/ a y)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+56) || !(z <= 2.3e-123)) {
		tmp = -4.5 * (z / (a / t));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.8d+56)) .or. (.not. (z <= 2.3d-123))) then
        tmp = (-4.5d0) * (z / (a / t))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+56) || !(z <= 2.3e-123)) {
		tmp = -4.5 * (z / (a / t));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+56) or not (z <= 2.3e-123):
		tmp = -4.5 * (z / (a / t))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e+56) || !(z <= 2.3e-123))
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.8e+56) || ~((z <= 2.3e-123)))
		tmp = -4.5 * (z / (a / t));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e+56], N[Not[LessEqual[z, 2.3e-123]], $MachinePrecision]], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999996e56 or 2.29999999999999987e-123 < z

   1. Initial program 88.4%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0 63.5%

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

      1. associate-*l/ 68.2%

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

   7. Simplified 68.2%

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

      1. *-commutative 68.2%

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

      2. clear-num 67.4%

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

      3. un-div-inv 67.7%

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

   9. Applied egg-rr 67.7%

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

   if -3.79999999999999996e56 < z < 2.29999999999999987e-123

   1. Initial program 97.3%

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

      1. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around inf 73.7%

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

      1. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+56} \lor \neg \left(z \leq 2.3 \cdot 10^{-123}\right):\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+50} \lor \neg \left(z \leq 9.2 \cdot 10^{-124}\right):\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+50) (not (<= z 9.2e-124)))
   (* -4.5 (/ z (/ a t)))
   (* 0.5 (/ (* x y) 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 ((z <= -9.5e+50) || !(z <= 9.2e-124)) {
		tmp = -4.5 * (z / (a / t));
	} else {
		tmp = 0.5 * ((x * y) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+50)) .or. (.not. (z <= 9.2d-124))) then
        tmp = (-4.5d0) * (z / (a / t))
    else
        tmp = 0.5d0 * ((x * y) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+50) || !(z <= 9.2e-124)) {
		tmp = -4.5 * (z / (a / t));
	} else {
		tmp = 0.5 * ((x * y) / 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 (z <= -9.5e+50) or not (z <= 9.2e-124):
		tmp = -4.5 * (z / (a / t))
	else:
		tmp = 0.5 * ((x * y) / 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 ((z <= -9.5e+50) || !(z <= 9.2e-124))
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	else
		tmp = Float64(0.5 * Float64(Float64(x * y) / 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 ((z <= -9.5e+50) || ~((z <= 9.2e-124)))
		tmp = -4.5 * (z / (a / t));
	else
		tmp = 0.5 * ((x * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+50], N[Not[LessEqual[z, 9.2e-124]], $MachinePrecision]], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999993e50 or 9.20000000000000048e-124 < z

   1. Initial program 88.4%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0 63.5%

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

      1. associate-*l/ 68.2%

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

   7. Simplified 68.2%

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

      1. *-commutative 68.2%

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

      2. clear-num 67.4%

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

      3. un-div-inv 67.7%

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

   9. Applied egg-rr 67.7%

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

   if -9.4999999999999993e50 < z < 9.20000000000000048e-124

   1. Initial program 97.3%

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

      1. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around inf 73.7%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+50} \lor \neg \left(z \leq 9.2 \cdot 10^{-124}\right):\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+51} \lor \neg \left(z \leq 2.3 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{t}}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e+51) (not (<= z 2.3e-123)))
   (/ -4.5 (/ (/ a t) z))
   (* 0.5 (/ (* x y) 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 ((z <= -6e+51) || !(z <= 2.3e-123)) {
		tmp = -4.5 / ((a / t) / z);
	} else {
		tmp = 0.5 * ((x * y) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6d+51)) .or. (.not. (z <= 2.3d-123))) then
        tmp = (-4.5d0) / ((a / t) / z)
    else
        tmp = 0.5d0 * ((x * y) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e+51) || !(z <= 2.3e-123)) {
		tmp = -4.5 / ((a / t) / z);
	} else {
		tmp = 0.5 * ((x * y) / 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 (z <= -6e+51) or not (z <= 2.3e-123):
		tmp = -4.5 / ((a / t) / z)
	else:
		tmp = 0.5 * ((x * y) / 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 ((z <= -6e+51) || !(z <= 2.3e-123))
		tmp = Float64(-4.5 / Float64(Float64(a / t) / z));
	else
		tmp = Float64(0.5 * Float64(Float64(x * y) / 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 ((z <= -6e+51) || ~((z <= 2.3e-123)))
		tmp = -4.5 / ((a / t) / z);
	else
		tmp = 0.5 * ((x * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e+51], N[Not[LessEqual[z, 2.3e-123]], $MachinePrecision]], N[(-4.5 / N[(N[(a / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6e51 or 2.29999999999999987e-123 < z

   1. Initial program 88.4%

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

      1. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0 63.5%

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

      1. associate-*l/ 68.2%

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

   7. Simplified 68.2%

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

      1. *-commutative 68.2%

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

      2. clear-num 67.4%

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

      3. un-div-inv 67.7%

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

   9. Applied egg-rr 67.7%

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

       1. clear-num 67.7%

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

       2. un-div-inv 67.8%

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

   11. Applied egg-rr 67.8%

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

   if -6e51 < z < 2.29999999999999987e-123

   1. Initial program 97.3%

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

      1. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around inf 73.7%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+51} \lor \neg \left(z \leq 2.3 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{t}}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+50}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-123}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

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 (<= z -7.5e+50)
   (* (* z -4.5) (/ t a))
   (if (<= z 2.3e-123) (* 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 (z <= -7.5e+50) {
		tmp = (z * -4.5) * (t / a);
	} else if (z <= 2.3e-123) {
		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 (z <= (-7.5d+50)) then
        tmp = (z * (-4.5d0)) * (t / a)
    else if (z <= 2.3d-123) 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 (z <= -7.5e+50) {
		tmp = (z * -4.5) * (t / a);
	} else if (z <= 2.3e-123) {
		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 z <= -7.5e+50:
		tmp = (z * -4.5) * (t / a)
	elif z <= 2.3e-123:
		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 (z <= -7.5e+50)
		tmp = Float64(Float64(z * -4.5) * Float64(t / a));
	elseif (z <= 2.3e-123)
		tmp = Float64(0.5 * Float64(Float64(x * 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 (z <= -7.5e+50)
		tmp = (z * -4.5) * (t / a);
	elseif (z <= 2.3e-123)
		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[z, -7.5e+50], N[(N[(z * -4.5), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-123], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.4999999999999999e50

   1. Initial program 93.1%

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

      1. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in x around 0 83.7%

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

      1. associate-*l/ 90.4%

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

   7. Simplified 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-/r/ 84.6%

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

      3. associate-*l/ 84.9%

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

   9. Applied egg-rr 84.9%

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

       1. associate-/r/ 90.5%

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

       2. *-commutative 90.5%

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

       3. *-un-lft-identity 90.5%

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

       4. times-frac 90.4%

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

       5. metadata-eval 90.4%

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

       6. clear-num 90.3%

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

       7. div-inv 90.5%

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

       8. *-commutative 90.5%

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

       9. associate-*r/ 90.6%

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

       10. div-inv 90.4%

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

       11. clear-num 90.4%

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

   11. Applied egg-rr 90.4%

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

   if -7.4999999999999999e50 < z < 2.29999999999999987e-123

   1. Initial program 97.3%

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

      1. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around inf 73.7%

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

   if 2.29999999999999987e-123 < z

   1. Initial program 86.4%

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

      1. associate-*l* 86.5%

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

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   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/ 59.0%

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

   7. Simplified 59.0%

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

      1. *-commutative 59.0%

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

      2. clear-num 58.0%

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

      3. un-div-inv 58.4%

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

   9. Applied egg-rr 58.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+50}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-123}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{z \cdot -4.5}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-124}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{t}}{z}}\\ \end{array} \end{array} \]

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 (<= z -6.5e+52)
   (/ (* z -4.5) (/ a t))
   (if (<= z 3.6e-124) (* 0.5 (/ (* x y) a)) (/ -4.5 (/ (/ a t) z)))))

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 (z <= -6.5e+52) {
		tmp = (z * -4.5) / (a / t);
	} else if (z <= 3.6e-124) {
		tmp = 0.5 * ((x * y) / a);
	} else {
		tmp = -4.5 / ((a / t) / z);
	}
	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 (z <= (-6.5d+52)) then
        tmp = (z * (-4.5d0)) / (a / t)
    else if (z <= 3.6d-124) then
        tmp = 0.5d0 * ((x * y) / a)
    else
        tmp = (-4.5d0) / ((a / t) / z)
    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 (z <= -6.5e+52) {
		tmp = (z * -4.5) / (a / t);
	} else if (z <= 3.6e-124) {
		tmp = 0.5 * ((x * y) / a);
	} else {
		tmp = -4.5 / ((a / t) / z);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+52:
		tmp = (z * -4.5) / (a / t)
	elif z <= 3.6e-124:
		tmp = 0.5 * ((x * y) / a)
	else:
		tmp = -4.5 / ((a / t) / z)
	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 (z <= -6.5e+52)
		tmp = Float64(Float64(z * -4.5) / Float64(a / t));
	elseif (z <= 3.6e-124)
		tmp = Float64(0.5 * Float64(Float64(x * y) / a));
	else
		tmp = Float64(-4.5 / Float64(Float64(a / t) / z));
	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 (z <= -6.5e+52)
		tmp = (z * -4.5) / (a / t);
	elseif (z <= 3.6e-124)
		tmp = 0.5 * ((x * y) / a);
	else
		tmp = -4.5 / ((a / t) / z);
	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[z, -6.5e+52], N[(N[(z * -4.5), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-124], N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 / N[(N[(a / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.49999999999999996e52

   1. Initial program 93.1%

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

      1. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in x around 0 83.7%

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

      1. associate-*l/ 90.4%

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

   7. Simplified 90.4%

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

      1. *-commutative 90.4%

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

      2. clear-num 90.2%

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

      3. un-div-inv 90.4%

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

   9. Applied egg-rr 90.4%

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

       1. associate-*r/ 90.6%

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

   11. Applied egg-rr 90.6%

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

   if -6.49999999999999996e52 < z < 3.6000000000000001e-124

   1. Initial program 97.3%

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

      1. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around inf 73.7%

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

   if 3.6000000000000001e-124 < z

   1. Initial program 86.4%

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

      1. associate-*l* 86.5%

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

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   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/ 59.0%

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

   7. Simplified 59.0%

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

      1. *-commutative 59.0%

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

      2. clear-num 58.0%

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

      3. un-div-inv 58.4%

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

   9. Applied egg-rr 58.4%

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

       1. clear-num 58.4%

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

       2. un-div-inv 58.4%

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

   11. Applied egg-rr 58.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{z \cdot -4.5}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-124}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{t}}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.2% accurate, 1.0× speedup

Math

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

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

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 = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
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 ((x * y) - (z * (9.0 * t))) / (a * 2.0);
}

Python

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

Julia

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

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
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[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.4%

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

   1. associate-*l* 92.4%

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

3. Simplified 92.4%

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

5. Final simplification 92.4%

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

Alternative 9: 51.2% 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 92.4%

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

   1. associate-*l* 92.4%

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

3. Simplified 92.4%

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

5. Taylor expanded in x around 0 49.9%

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

   1. associate-*l/ 51.4%

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

7. Simplified 51.4%

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

8. Final simplification 51.4%

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

Alternative 10: 51.1% accurate, 1.9× speedup

Math

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

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 (/ a t))))

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 / (a / t));
}

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 / (a / t))
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 / (a / t));
}

Python

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

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

Derivation

1. Initial program 92.4%

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

   1. associate-*l* 92.4%

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

3. Simplified 92.4%

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

5. Taylor expanded in x around 0 49.9%

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

   1. associate-*l/ 51.4%

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

7. Simplified 51.4%

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

   1. *-commutative 51.4%

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

   2. clear-num 51.0%

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

   3. un-div-inv 51.2%

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

9. Applied egg-rr 51.2%

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

10. Final simplification 51.2%

    \[\leadsto -4.5 \cdot \frac{z}{\frac{a}{t}} \]
11. 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 2024021 
(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)))