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

Average Accuracy: 68.2% → 83.6%

Time: 28.0s

Precision: binary64

Cost: 2640

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

Math

\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

↓

\[\begin{array}{l} t_1 := \frac{a \cdot \left(t \cdot -4\right) + \frac{x \cdot \left(9 \cdot y\right) + b}{z}}{c}\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+243}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{elif}\;t_2 \leq -0.001:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{elif}\;t_2 \leq 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* a (* t -4.0)) (/ (+ (* x (* 9.0 y)) b) z)) c))
        (t_2 (* (* x 9.0) y)))
   (if (<= t_2 -5e+243)
     (* 9.0 (/ x (/ z (/ y c))))
     (if (<= t_2 -0.001)
       t_1
       (if (<= t_2 -4e-38)
         (+ (* -4.0 (/ a (/ c t))) (/ b (* z c)))
         (if (<= t_2 1e+209) t_1 (* 9.0 (/ y (* z (/ c x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a * (t * -4.0)) + (((x * (9.0 * y)) + b) / z)) / c;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -5e+243) {
		tmp = 9.0 * (x / (z / (y / c)));
	} else if (t_2 <= -0.001) {
		tmp = t_1;
	} else if (t_2 <= -4e-38) {
		tmp = (-4.0 * (a / (c / t))) + (b / (z * c));
	} else if (t_2 <= 1e+209) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (y / (z * (c / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

↓

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * (t * (-4.0d0))) + (((x * (9.0d0 * y)) + b) / z)) / c
    t_2 = (x * 9.0d0) * y
    if (t_2 <= (-5d+243)) then
        tmp = 9.0d0 * (x / (z / (y / c)))
    else if (t_2 <= (-0.001d0)) then
        tmp = t_1
    else if (t_2 <= (-4d-38)) then
        tmp = ((-4.0d0) * (a / (c / t))) + (b / (z * c))
    else if (t_2 <= 1d+209) then
        tmp = t_1
    else
        tmp = 9.0d0 * (y / (z * (c / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a * (t * -4.0)) + (((x * (9.0 * y)) + b) / z)) / c;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -5e+243) {
		tmp = 9.0 * (x / (z / (y / c)));
	} else if (t_2 <= -0.001) {
		tmp = t_1;
	} else if (t_2 <= -4e-38) {
		tmp = (-4.0 * (a / (c / t))) + (b / (z * c));
	} else if (t_2 <= 1e+209) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (y / (z * (c / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

↓

def code(x, y, z, t, a, b, c):
	t_1 = ((a * (t * -4.0)) + (((x * (9.0 * y)) + b) / z)) / c
	t_2 = (x * 9.0) * y
	tmp = 0
	if t_2 <= -5e+243:
		tmp = 9.0 * (x / (z / (y / c)))
	elif t_2 <= -0.001:
		tmp = t_1
	elif t_2 <= -4e-38:
		tmp = (-4.0 * (a / (c / t))) + (b / (z * c))
	elif t_2 <= 1e+209:
		tmp = t_1
	else:
		tmp = 9.0 * (y / (z * (c / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

↓

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(Float64(Float64(x * Float64(9.0 * y)) + b) / z)) / c)
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -5e+243)
		tmp = Float64(9.0 * Float64(x / Float64(z / Float64(y / c))));
	elseif (t_2 <= -0.001)
		tmp = t_1;
	elseif (t_2 <= -4e-38)
		tmp = Float64(Float64(-4.0 * Float64(a / Float64(c / t))) + Float64(b / Float64(z * c)));
	elseif (t_2 <= 1e+209)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

↓

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((a * (t * -4.0)) + (((x * (9.0 * y)) + b) / z)) / c;
	t_2 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_2 <= -5e+243)
		tmp = 9.0 * (x / (z / (y / c)));
	elseif (t_2 <= -0.001)
		tmp = t_1;
	elseif (t_2 <= -4e-38)
		tmp = (-4.0 * (a / (c / t))) + (b / (z * c));
	elseif (t_2 <= 1e+209)
		tmp = t_1;
	else
		tmp = 9.0 * (y / (z * (c / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+243], N[(9.0 * N[(x / N[(z / N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -0.001], t$95$1, If[LessEqual[t$95$2, -4e-38], N[(N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+209], t$95$1, N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	68.2%
Target	77.5%
Herbie	83.6%

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x 9) y) < -5.00000000000000037e243

   1. Initial program 28.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 27.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      Proof

      [Start] 28.9	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 22.0	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in x around inf 28.6%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]

   4. Simplified 73.0%

      \[\leadsto \color{blue}{9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}} \]
      Proof

      [Start] 28.6	\[ 9 \cdot \frac{y \cdot x}{c \cdot z} \]
      *-commutative [=>] 28.6	\[ 9 \cdot \frac{\color{blue}{x \cdot y}}{c \cdot z} \]
      associate-/l* [=>] 60.8	\[ 9 \cdot \color{blue}{\frac{x}{\frac{c \cdot z}{y}}} \]
      *-commutative [=>] 60.8	\[ 9 \cdot \frac{x}{\frac{\color{blue}{z \cdot c}}{y}} \]
      associate-/l* [=>] 73.0	\[ 9 \cdot \frac{x}{\color{blue}{\frac{z}{\frac{y}{c}}}} \]

   if -5.00000000000000037e243 < (*.f64 (*.f64 x 9) y) < -1e-3 or -3.9999999999999998e-38 < (*.f64 (*.f64 x 9) y) < 1.0000000000000001e209

   1. Initial program 73.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}} \]
      Proof

      [Start] 73.5	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 71.6	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied egg-rr 86.0%

      \[\leadsto \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z}}{c} \]
      Proof

      [Start] 86.0	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c} \]
      fma-udef [=>] 86.0	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z}}{c} \]

   if -1e-3 < (*.f64 (*.f64 x 9) y) < -3.9999999999999998e-38

   1. Initial program 80.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}} \]
      Proof

      [Start] 80.2	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 74.4	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in x around 0 61.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}} \]

   4. Taylor expanded in b around 0 66.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}} \]

   5. Simplified 70.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{c \cdot z}} \]
      Proof

      [Start] 66.5	\[ \frac{b}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c} \]
      +-commutative [=>] 66.5	\[ \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}} \]
      associate-/l* [=>] 70.1	\[ -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} + \frac{b}{c \cdot z} \]

   if 1.0000000000000001e209 < (*.f64 (*.f64 x 9) y)

   1. Initial program 32.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 39.9%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}} \]
      Proof

      [Start] 32.0	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 29.6	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied egg-rr 39.9%

      \[\leadsto \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z}}{c} \]
      Proof

      [Start] 39.9	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c} \]
      fma-udef [=>] 39.9	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z}}{c} \]

   4. Taylor expanded in x around inf 31.8%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]

   5. Simplified 69.2%

      \[\leadsto \color{blue}{9 \cdot \frac{y}{\frac{c}{x} \cdot z}} \]
      Proof

      [Start] 31.8	\[ 9 \cdot \frac{y \cdot x}{c \cdot z} \]
      associate-/l* [=>] 57.2	\[ 9 \cdot \color{blue}{\frac{y}{\frac{c \cdot z}{x}}} \]
      associate-/l* [=>] 67.4	\[ 9 \cdot \frac{y}{\color{blue}{\frac{c}{\frac{x}{z}}}} \]
      associate-/r/ [=>] 69.2	\[ 9 \cdot \frac{y}{\color{blue}{\frac{c}{x} \cdot z}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -5 \cdot 10^{+243}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq -0.001:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{x \cdot \left(9 \cdot y\right) + b}{z}}{c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq -4 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq 10^{+209}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{x \cdot \left(9 \cdot y\right) + b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	64.4%
Cost	2148

\[\begin{array}{l} t_1 := \frac{a \cdot \left(t \cdot -4\right) + \frac{x \cdot y}{\frac{z}{9}}}{c}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+214}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+171}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+71}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-167}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \end{array} \]

Alternative 2
Accuracy	56.3%
Cost	1900

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{-55}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-187}:\\ \;\;\;\;\frac{\frac{9 \cdot y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{\frac{t}{\frac{c}{-4}}}{\frac{1}{a}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+254}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 3
Accuracy	67.5%
Cost	1625

\[\begin{array}{l} t_1 := \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-187}:\\ \;\;\;\;\frac{\frac{9 \cdot y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+173} \lor \neg \left(a \leq 2 \cdot 10^{+239}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]

Alternative 4
Accuracy	67.5%
Cost	1625

\[\begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-212}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{9 \cdot y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+172} \lor \neg \left(a \leq 9.2 \cdot 10^{+237}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]

Alternative 5
Accuracy	44.6%
Cost	1500

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -6 \cdot 10^{-184}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-268}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 6.6:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 6
Accuracy	44.5%
Cost	1500

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-183}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-267}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 0.186:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 7
Accuracy	43.8%
Cost	1500

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{-183}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-269}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-32}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 0.195:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 8
Accuracy	43.8%
Cost	1500

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-183}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-268}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-54}:\\ \;\;\;\;\frac{9}{\frac{z}{x} \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.1:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 9
Accuracy	64.6%
Cost	1364

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{+213}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+168}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+82}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \end{array} \]

Alternative 10
Accuracy	45.3%
Cost	977

\[\begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-155} \lor \neg \left(t \leq 5.9 \cdot 10^{-164}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 11
Accuracy	45.5%
Cost	977

\[\begin{array}{l} \mathbf{if}\;t \leq -1.76 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-154} \lor \neg \left(t \leq 8.6 \cdot 10^{-164}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 12
Accuracy	45.5%
Cost	976

\[\begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-154}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-164}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 13
Accuracy	45.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-184} \lor \neg \left(a \leq 3.2 \cdot 10^{-65}\right):\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 14
Accuracy	32.9%
Cost	452

\[\begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 15
Accuracy	32.8%
Cost	452

\[\begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 16
Accuracy	32.1%
Cost	320

\[\frac{b}{z \cdot c} \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))