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

Percentage Accurate: 95.2% → 95.9%

Time: 10.4s

Precision: binary64

Cost: 969

• 28.3% of points produce a very large (infinite) output. You may want to add a precondition.

Math

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

↓

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-188} \lor \neg \left(y \leq 3.6 \cdot 10^{-251}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

↓

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.4e-188) (not (<= y 3.6e-251)))
   (+ x (/ (- y (/ t y)) (* z -3.0)))
   (+ x (/ t (* z (* 3.0 y))))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e-188) || !(y <= 3.6e-251)) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = x + (t / (z * (3.0 * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.4d-188)) .or. (.not. (y <= 3.6d-251))) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    else
        tmp = x + (t / (z * (3.0d0 * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e-188) || !(y <= 3.6e-251)) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = x + (t / (z * (3.0 * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

↓

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.4e-188) or not (y <= 3.6e-251):
		tmp = x + ((y - (t / y)) / (z * -3.0))
	else:
		tmp = x + (t / (z * (3.0 * y)))
	return tmp

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

↓

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.4e-188) || !(y <= 3.6e-251))
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(t / Float64(z * Float64(3.0 * y))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.4e-188) || ~((y <= 3.6e-251)))
		tmp = x + ((y - (t / y)) / (z * -3.0));
	else
		tmp = x + (t / (z * (3.0 * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.4e-188], N[Not[LessEqual[y, 3.6e-251]], $MachinePrecision]], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	95.2%
Target	95.5%
Herbie	95.9%

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \]

Derivation

1. Split input into 2 regimes

2. if y < -6.40000000000000044e-188 or 3.6000000000000001e-251 < y

   1. Initial program 94.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Simplified 98.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
      Step-by-step derivation

      [Start] 94.1%	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 94.1%	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 94.1%	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      sub-neg [=>] 94.1%	\[ x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]
      distribute-neg-in [=>] 94.1%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      unsub-neg [=>] 94.1%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 94.1%	\[ x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*r/ [=>] 94.1%	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*l/ [<=] 94.0%	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      distribute-neg-frac [=>] 94.0%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      neg-mul-1 [=>] 94.0%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]
      times-frac [=>] 97.4%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 98.8%	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 98.8%	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 98.8%	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 98.8%	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{\frac{y - \frac{t}{y}}{z \cdot -3}} \]
      Step-by-step derivation

      [Start] 98.8%	\[ x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right) \]
      *-commutative [=>] 98.8%	\[ x + \color{blue}{\left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}} \]
      clear-num [=>] 98.8%	\[ x + \left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \]
      un-div-inv [=>] 98.9%	\[ x + \color{blue}{\frac{y - \frac{t}{y}}{\frac{z}{-0.3333333333333333}}} \]
      div-inv [=>] 98.9%	\[ x + \frac{y - \frac{t}{y}}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}} \]
      metadata-eval [=>] 98.9%	\[ x + \frac{y - \frac{t}{y}}{z \cdot \color{blue}{-3}} \]

   if -6.40000000000000044e-188 < y < 3.6000000000000001e-251

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Simplified 75.6%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
      Step-by-step derivation

      [Start] 99.8%	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 99.8%	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 99.8%	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      sub-neg [=>] 99.8%	\[ x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]
      distribute-neg-in [=>] 99.8%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      unsub-neg [=>] 99.8%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 99.8%	\[ x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*r/ [=>] 99.8%	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*l/ [<=] 99.8%	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      distribute-neg-frac [=>] 99.8%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      neg-mul-1 [=>] 99.8%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]
      times-frac [=>] 75.6%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 75.6%	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 75.6%	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 75.6%	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 75.6%	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Taylor expanded in y around 0 99.7%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]

   4. Simplified 75.6%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]
      Step-by-step derivation

      [Start] 99.7%	\[ x + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]
      *-commutative [=>] 99.7%	\[ x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]
      associate-*l/ [=>] 99.8%	\[ x + \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]
      times-frac [=>] 75.6%	\[ x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}} \]
      Step-by-step derivation

      [Start] 75.6%	\[ x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z} \]
      *-commutative [=>] 75.6%	\[ x + \color{blue}{\frac{0.3333333333333333}{z} \cdot \frac{t}{y}} \]
      clear-num [=>] 75.6%	\[ x + \color{blue}{\frac{1}{\frac{z}{0.3333333333333333}}} \cdot \frac{t}{y} \]
      frac-times [=>] 99.7%	\[ x + \color{blue}{\frac{1 \cdot t}{\frac{z}{0.3333333333333333} \cdot y}} \]
      *-un-lft-identity [<=] 99.7%	\[ x + \frac{\color{blue}{t}}{\frac{z}{0.3333333333333333} \cdot y} \]
      div-inv [=>] 99.8%	\[ x + \frac{t}{\color{blue}{\left(z \cdot \frac{1}{0.3333333333333333}\right)} \cdot y} \]
      metadata-eval [=>] 99.8%	\[ x + \frac{t}{\left(z \cdot \color{blue}{3}\right) \cdot y} \]

   6. Taylor expanded in z around 0 99.8%

      \[\leadsto x + \frac{t}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

   7. Simplified 99.9%

      \[\leadsto x + \frac{t}{\color{blue}{z \cdot \left(y \cdot 3\right)}} \]
      Step-by-step derivation

      [Start] 99.8%	\[ x + \frac{t}{3 \cdot \left(y \cdot z\right)} \]
      associate-*r* [=>] 99.9%	\[ x + \frac{t}{\color{blue}{\left(3 \cdot y\right) \cdot z}} \]
      *-commutative [<=] 99.9%	\[ x + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
      *-commutative [=>] 99.9%	\[ x + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-188} \lor \neg \left(y \leq 3.6 \cdot 10^{-251}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	95.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-188} \lor \neg \left(y \leq 3.6 \cdot 10^{-251}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \]

Alternative 2
Accuracy	97.3%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 5 \cdot 10^{-119}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t}{z \cdot \left(3 \cdot y\right)} - \frac{y}{z} \cdot 0.3333333333333333\right)\\ \end{array} \]

Alternative 3
Accuracy	97.2%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 5 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternative 4
Accuracy	60.4%
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{\frac{z}{-0.3333333333333333}}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-17}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot y}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 5
Accuracy	60.2%
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+112}:\\ \;\;\;\;\frac{y}{\frac{z}{-0.3333333333333333}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+41}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot y}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 6
Accuracy	87.4%
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 7
Accuracy	95.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-185} \lor \neg \left(y \leq 7.8 \cdot 10^{-265}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \]

Alternative 8
Accuracy	76.1%
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-92}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-265}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{0.3333333333333333}{z}}{\frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 9
Accuracy	80.5%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+86}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \end{array} \]

Alternative 10
Accuracy	87.8%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+59}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 11
Accuracy	88.2%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+58}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 12
Accuracy	75.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-92} \lor \neg \left(y \leq 5.6 \cdot 10^{-39}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 13
Accuracy	75.8%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 14
Accuracy	75.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-92}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 15
Accuracy	46.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -14600000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+157}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Accuracy	46.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -550:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+157}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Accuracy	29.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023167 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))