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

Average Accuracy: 94.4% → 98.4%

Time: 16.5s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+93}:\\ \;\;\;\;t_1 + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

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
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= (* z 3.0) -2e+93)
     (+ t_1 (/ t (* z (* 3.0 y))))
     (if (<= (* z 3.0) 4e-34)
       (+ x (/ 0.3333333333333333 (/ z (- (/ t y) y))))
       (+ t_1 (/ (/ 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 t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -2e+93) {
		tmp = t_1 + (t / (z * (3.0 * y)));
	} else if ((z * 3.0) <= 4e-34) {
		tmp = x + (0.3333333333333333 / (z / ((t / y) - y)));
	} else {
		tmp = t_1 + ((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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if ((z * 3.0d0) <= (-2d+93)) then
        tmp = t_1 + (t / (z * (3.0d0 * y)))
    else if ((z * 3.0d0) <= 4d-34) then
        tmp = x + (0.3333333333333333d0 / (z / ((t / y) - y)))
    else
        tmp = t_1 + ((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 t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -2e+93) {
		tmp = t_1 + (t / (z * (3.0 * y)));
	} else if ((z * 3.0) <= 4e-34) {
		tmp = x + (0.3333333333333333 / (z / ((t / y) - y)));
	} else {
		tmp = t_1 + ((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):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if (z * 3.0) <= -2e+93:
		tmp = t_1 + (t / (z * (3.0 * y)))
	elif (z * 3.0) <= 4e-34:
		tmp = x + (0.3333333333333333 / (z / ((t / y) - y)))
	else:
		tmp = t_1 + ((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)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+93)
		tmp = Float64(t_1 + Float64(t / Float64(z * Float64(3.0 * y))));
	elseif (Float64(z * 3.0) <= 4e-34)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(z / Float64(Float64(t / y) - y))));
	else
		tmp = Float64(t_1 + Float64(Float64(t / Float64(z * 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)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if ((z * 3.0) <= -2e+93)
		tmp = t_1 + (t / (z * (3.0 * y)));
	elseif ((z * 3.0) <= 4e-34)
		tmp = x + (0.3333333333333333 / (z / ((t / y) - y)));
	else
		tmp = t_1 + ((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_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+93], N[(t$95$1 + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 4e-34], N[(x + N[(0.3333333333333333 / N[(z / N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	94.4%
Target	97.2%
Herbie	98.4%

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -2.00000000000000009e93

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 99.2%

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

   3. Simplified 99.2%

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

      [Start] 99.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{3 \cdot \left(y \cdot z\right)} \]
      associate-*r* [=>] 99.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(3 \cdot y\right) \cdot z}} \]
      *-commutative [<=] 99.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
      *-commutative [=>] 99.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   if -2.00000000000000009e93 < (*.f64 z 3) < 3.99999999999999971e-34

   1. Initial program 87.2%

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

   2. Simplified 95.8%

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

      [Start] 87.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-/r* [=>] 95.8	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   3. Taylor expanded in x around 0 86.8%

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

   4. Simplified 98.5%

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

      [Start] 86.8	\[ \left(0.3333333333333333 \cdot \frac{t}{y \cdot z} + x\right) - 0.3333333333333333 \cdot \frac{y}{z} \]
      cancel-sign-sub-inv [=>] 86.8	\[ \color{blue}{\left(0.3333333333333333 \cdot \frac{t}{y \cdot z} + x\right) + \left(-0.3333333333333333\right) \cdot \frac{y}{z}} \]
      metadata-eval [=>] 86.8	\[ \left(0.3333333333333333 \cdot \frac{t}{y \cdot z} + x\right) + \color{blue}{-0.3333333333333333} \cdot \frac{y}{z} \]
      +-commutative [=>] 86.8	\[ \color{blue}{\left(x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\right)} + -0.3333333333333333 \cdot \frac{y}{z} \]
      associate-*r/ [=>] 86.9	\[ \left(x + \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}}\right) + -0.3333333333333333 \cdot \frac{y}{z} \]
      associate-*l/ [<=] 85.5	\[ \left(x + \color{blue}{\frac{0.3333333333333333}{y \cdot z} \cdot t}\right) + -0.3333333333333333 \cdot \frac{y}{z} \]
      *-commutative [=>] 85.5	\[ \left(x + \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}}\right) + -0.3333333333333333 \cdot \frac{y}{z} \]
      associate-+l+ [=>] 85.5	\[ \color{blue}{x + \left(t \cdot \frac{0.3333333333333333}{y \cdot z} + -0.3333333333333333 \cdot \frac{y}{z}\right)} \]
      metadata-eval [<=] 85.5	\[ x + \left(t \cdot \frac{0.3333333333333333}{y \cdot z} + \color{blue}{\left(-0.3333333333333333\right)} \cdot \frac{y}{z}\right) \]
      cancel-sign-sub-inv [<=] 85.5	\[ x + \color{blue}{\left(t \cdot \frac{0.3333333333333333}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z}\right)} \]
      *-commutative [<=] 85.5	\[ x + \left(\color{blue}{\frac{0.3333333333333333}{y \cdot z} \cdot t} - 0.3333333333333333 \cdot \frac{y}{z}\right) \]
      associate-*l/ [=>] 86.9	\[ x + \left(\color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} - 0.3333333333333333 \cdot \frac{y}{z}\right) \]
      associate-*r/ [<=] 86.8	\[ x + \left(\color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} - 0.3333333333333333 \cdot \frac{y}{z}\right) \]
      associate-/r* [=>] 98.3	\[ x + \left(0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{y}}{z}} - 0.3333333333333333 \cdot \frac{y}{z}\right) \]
      associate-*r/ [=>] 98.4	\[ x + \left(\color{blue}{\frac{0.3333333333333333 \cdot \frac{t}{y}}{z}} - 0.3333333333333333 \cdot \frac{y}{z}\right) \]
      associate-*r/ [=>] 98.5	\[ x + \left(\frac{0.3333333333333333 \cdot \frac{t}{y}}{z} - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}}\right) \]
      div-sub [<=] 98.5	\[ x + \color{blue}{\frac{0.3333333333333333 \cdot \frac{t}{y} - 0.3333333333333333 \cdot y}{z}} \]
      distribute-lft-out-- [=>] 98.5	\[ x + \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]
      associate-/l* [=>] 98.5	\[ x + \color{blue}{\frac{0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}} \]

   if 3.99999999999999971e-34 < (*.f64 z 3)

   1. Initial program 99.1%

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

   2. Simplified 97.9%

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

      [Start] 99.1	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-/r* [=>] 97.9	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+93}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.9%
Cost	1480

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+93}:\\ \;\;\;\;t_1 + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{z}{\frac{t}{y} - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternative 2
Accuracy	56.2%
Cost	1244

\[\begin{array}{l} t_1 := y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -360:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-241}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{elif}\;x \leq 16000:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	56.4%
Cost	1244

\[\begin{array}{l} t_1 := y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -112:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.92 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-241}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{elif}\;x \leq 2800000:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	99.2%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-37} \lor \neg \left(t \leq 3.9 \cdot 10^{+58}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \end{array} \]

Alternative 5
Accuracy	57.1%
Cost	980

\[\begin{array}{l} t_1 := y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;x \leq -3 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.04 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-78}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 210000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	93.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-101} \lor \neg \left(y \leq -1.52 \cdot 10^{-167}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \]

Alternative 7
Accuracy	93.7%
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-164}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 8
Accuracy	57.1%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -14.5:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1000000000:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	81.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-107} \lor \neg \left(x \leq 5 \cdot 10^{-111}\right):\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]

Alternative 10
Accuracy	74.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-290} \lor \neg \left(y \leq 4.65 \cdot 10^{-138}\right):\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]

Alternative 11
Accuracy	74.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-289}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-143}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]

Alternative 12
Accuracy	74.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-143}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \]

Alternative 13
Accuracy	74.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \]

Alternative 14
Accuracy	74.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-291}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-143}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \]

Alternative 15
Accuracy	56.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 16000000:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Accuracy	42.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(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))))