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

Average Accuracy: 88.1% → 98.4%

Time: 20.6s

Precision: binary64

Cost: 2377

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y + t \cdot \left(z \cdot -9\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+248} \lor \neg \left(t_1 \leq 5 \cdot 10^{+198}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* t (* z -9.0)))))
   (if (or (<= t_1 -5e+248) (not (<= t_1 5e+198)))
     (- (* x (* y (/ 0.5 a))) (* (/ z a) (/ 9.0 (/ 2.0 t))))
     (+ (* -4.5 (/ (* z t) a)) (* 0.5 (/ (* x y) a))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) + (t * (z * -9.0));
	double tmp;
	if ((t_1 <= -5e+248) || !(t_1 <= 5e+198)) {
		tmp = (x * (y * (0.5 / a))) - ((z / a) * (9.0 / (2.0 / t)));
	} else {
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * ((x * y) / a));
	}
	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
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (t * (z * (-9.0d0)))
    if ((t_1 <= (-5d+248)) .or. (.not. (t_1 <= 5d+198))) then
        tmp = (x * (y * (0.5d0 / a))) - ((z / a) * (9.0d0 / (2.0d0 / t)))
    else
        tmp = ((-4.5d0) * ((z * t) / a)) + (0.5d0 * ((x * y) / a))
    end if
    code = tmp
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);
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) + (t * (z * -9.0));
	double tmp;
	if ((t_1 <= -5e+248) || !(t_1 <= 5e+198)) {
		tmp = (x * (y * (0.5 / a))) - ((z / a) * (9.0 / (2.0 / t)));
	} else {
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * ((x * y) / a));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = (x * y) + (t * (z * -9.0))
	tmp = 0
	if (t_1 <= -5e+248) or not (t_1 <= 5e+198):
		tmp = (x * (y * (0.5 / a))) - ((z / a) * (9.0 / (2.0 / t)))
	else:
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * ((x * y) / a))
	return tmp

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) + Float64(t * Float64(z * -9.0)))
	tmp = 0.0
	if ((t_1 <= -5e+248) || !(t_1 <= 5e+198))
		tmp = Float64(Float64(x * Float64(y * Float64(0.5 / a))) - Float64(Float64(z / a) * Float64(9.0 / Float64(2.0 / t))));
	else
		tmp = Float64(Float64(-4.5 * Float64(Float64(z * t) / a)) + Float64(0.5 * Float64(Float64(x * y) / a)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) + (t * (z * -9.0));
	tmp = 0.0;
	if ((t_1 <= -5e+248) || ~((t_1 <= 5e+198)))
		tmp = (x * (y * (0.5 / a))) - ((z / a) * (9.0 / (2.0 / t)));
	else
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * ((x * y) / a));
	end
	tmp_2 = tmp;
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]

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+248], N[Not[LessEqual[t$95$1, 5e+198]], $MachinePrecision]], N[(N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * N[(9.0 / N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	88.1%
Target	92.0%
Herbie	98.4%

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -4.9999999999999996e248 or 5.00000000000000049e198 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 49.5%

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

   2. Simplified 49.8%

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

      [Start] 49.5	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      associate-*l* [=>] 49.8	\[ \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Applied egg-rr 73.8%

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

      [Start] 49.8	\[ \frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2} \]
      div-sub [=>] 49.8	\[ \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
      sub-neg [=>] 49.8	\[ \color{blue}{\frac{x \cdot y}{a \cdot 2} + \left(-\frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\right)} \]
      div-inv [=>] 49.8	\[ \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{a \cdot 2}} + \left(-\frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\right) \]
      *-commutative [=>] 49.8	\[ \left(x \cdot y\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} + \left(-\frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\right) \]
      associate-/r* [=>] 49.8	\[ \left(x \cdot y\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} + \left(-\frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\right) \]
      metadata-eval [=>] 49.8	\[ \left(x \cdot y\right) \cdot \frac{\color{blue}{0.5}}{a} + \left(-\frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\right) \]
      times-frac [=>] 73.8	\[ \left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\color{blue}{\frac{z}{a} \cdot \frac{9 \cdot t}{2}}\right) \]

   4. Simplified 98.0%

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

      [Start] 73.8	\[ \left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\frac{z}{a} \cdot \frac{9 \cdot t}{2}\right) \]
      sub-neg [<=] 73.8	\[ \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a} - \frac{z}{a} \cdot \frac{9 \cdot t}{2}} \]
      associate-*l* [=>] 98.0	\[ \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} - \frac{z}{a} \cdot \frac{9 \cdot t}{2} \]
      associate-/l* [=>] 98.0	\[ x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \color{blue}{\frac{9}{\frac{2}{t}}} \]

   if -4.9999999999999996e248 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5.00000000000000049e198

   1. Initial program 98.5%

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

   2. Simplified 98.4%

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

      [Start] 98.5	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      sub-neg [=>] 98.5	\[ \frac{\color{blue}{x \cdot y + \left(-\left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]
      remove-double-neg [<=] 98.5	\[ \frac{\color{blue}{\left(-\left(-x \cdot y\right)\right)} + \left(-\left(z \cdot 9\right) \cdot t\right)}{a \cdot 2} \]
      distribute-neg-in [<=] 98.5	\[ \frac{\color{blue}{-\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]
      +-commutative [<=] 98.5	\[ \frac{-\color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)}}{a \cdot 2} \]
      sub-neg [<=] 98.5	\[ \frac{-\color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      neg-mul-1 [=>] 98.5	\[ \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      associate-/l* [=>] 98.0	\[ \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]
      associate-/r/ [=>] 98.4	\[ \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]
      sub-neg [=>] 98.4	\[ \frac{-1}{a \cdot 2} \cdot \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \]
      +-commutative [=>] 98.4	\[ \frac{-1}{a \cdot 2} \cdot \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \]
      neg-sub0 [=>] 98.4	\[ \frac{-1}{a \cdot 2} \cdot \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \]
      associate-+l- [=>] 98.4	\[ \frac{-1}{a \cdot 2} \cdot \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \]
      sub0-neg [=>] 98.4	\[ \frac{-1}{a \cdot 2} \cdot \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \]
      distribute-rgt-neg-out [=>] 98.4	\[ \color{blue}{-\frac{-1}{a \cdot 2} \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)} \]
      distribute-lft-neg-in [=>] 98.4	\[ \color{blue}{\left(-\frac{-1}{a \cdot 2}\right) \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)} \]

   3. Taylor expanded in x around 0 98.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{y \cdot x}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + t \cdot \left(z \cdot -9\right) \leq -5 \cdot 10^{+248} \lor \neg \left(x \cdot y + t \cdot \left(z \cdot -9\right) \leq 5 \cdot 10^{+198}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	93.5%
Cost	2760

\[\begin{array}{l} t_1 := \frac{x \cdot y + t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;t_1 \leq 10^{+304}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 2
Accuracy	93.4%
Cost	2632

\[\begin{array}{l} t_1 := \frac{x \cdot y + t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;t_1 \leq 10^{+304}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 3
Accuracy	63.8%
Cost	1768

\[\begin{array}{l} t_1 := z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ t_2 := z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{0.5}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-205}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-157}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-88}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-25}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 0.0058:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 4
Accuracy	64.0%
Cost	1636

\[\begin{array}{l} t_1 := z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{0.5}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-205}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-158}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-89}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-25}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 0.021:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{t \cdot -4.5}}\\ \end{array} \]

Alternative 5
Accuracy	64.0%
Cost	1636

\[\begin{array}{l} t_1 := z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \frac{0.5}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-208}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-158}:\\ \;\;\;\;\frac{x \cdot y}{\frac{a}{0.5}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-89}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-25}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 0.017:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{t \cdot -4.5}}\\ \end{array} \]

Alternative 6
Accuracy	60.2%
Cost	1240

\[\begin{array}{l} t_1 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ t_2 := -4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-141}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	60.6%
Cost	1240

\[\begin{array}{l} t_1 := -4.5 \cdot \frac{t}{\frac{a}{z}}\\ t_2 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+74}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-141}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	60.5%
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ t_2 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+74}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-140}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 9
Accuracy	60.5%
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ t_2 := y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+74}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-141}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 10
Accuracy	88.7%
Cost	1229

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+259} \lor \neg \left(y \leq 10^{+291}\right):\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + \left(z \cdot t\right) \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]

Alternative 11
Accuracy	63.6%
Cost	1108

\[\begin{array}{l} t_1 := z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-31}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 0.0105:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 12
Accuracy	63.8%
Cost	1108

\[\begin{array}{l} t_1 := z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 0.011:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+246}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 13
Accuracy	51.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+88} \lor \neg \left(a \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 14
Accuracy	49.1%
Cost	448

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

Reproduce

herbie shell --seed 2023138 
(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)))