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

Average Error: 5.55% → 1.21%

Time: 17.2s

Precision: binary64

Cost: 1224

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+137}:\\ \;\;\;\;\frac{t}{z \cdot \left(y \cdot 3\right)} + t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

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 (<= t -9e+137)
     (+ (/ t (* z (* y 3.0))) t_1)
     (if (<= t 5e-8)
       (+ x (/ (- y (/ t y)) (* z -3.0)))
       (+ t_1 (/ t (* y (* z 3.0))))))))

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 (t <= -9e+137) {
		tmp = (t / (z * (y * 3.0))) + t_1;
	} else if (t <= 5e-8) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = t_1 + (t / (y * (z * 3.0)));
	}
	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 (t <= (-9d+137)) then
        tmp = (t / (z * (y * 3.0d0))) + t_1
    else if (t <= 5d-8) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    else
        tmp = t_1 + (t / (y * (z * 3.0d0)))
    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 (t <= -9e+137) {
		tmp = (t / (z * (y * 3.0))) + t_1;
	} else if (t <= 5e-8) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = t_1 + (t / (y * (z * 3.0)));
	}
	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 t <= -9e+137:
		tmp = (t / (z * (y * 3.0))) + t_1
	elif t <= 5e-8:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	else:
		tmp = t_1 + (t / (y * (z * 3.0)))
	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 (t <= -9e+137)
		tmp = Float64(Float64(t / Float64(z * Float64(y * 3.0))) + t_1);
	elseif (t <= 5e-8)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	else
		tmp = Float64(t_1 + Float64(t / Float64(y * Float64(z * 3.0))));
	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 (t <= -9e+137)
		tmp = (t / (z * (y * 3.0))) + t_1;
	elseif (t <= 5e-8)
		tmp = x + ((y - (t / y)) / (z * -3.0));
	else
		tmp = t_1 + (t / (y * (z * 3.0)));
	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[t, -9e+137], N[(N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 5e-8], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	5.55%
Target	2.5%
Herbie	1.21%

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

Derivation

1. Split input into 3 regimes

2. if t < -9.0000000000000003e137

   1. Initial program 1.47

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

   2. Taylor expanded in z around 0 1.46

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

   3. Simplified 1.47

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

      [Start] 1.46	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{3 \cdot \left(y \cdot z\right)} \]
      associate-*r* [=>] 1.47	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(3 \cdot y\right) \cdot z}} \]
      *-commutative [<=] 1.47	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
      *-commutative [=>] 1.47	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   if -9.0000000000000003e137 < t < 4.9999999999999998e-8

   1. Initial program 7.63

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

   2. Simplified 1.3

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

      [Start] 7.63	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 7.63	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 7.63	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 7.63	\[ x + \color{blue}{-1 \cdot \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      distribute-lft-out-- [<=] 7.63	\[ x + \color{blue}{\left(-1 \cdot \frac{y}{z \cdot 3} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      associate-*r/ [=>] 7.63	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*l/ [<=] 7.68	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*r/ [=>] 7.68	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1 \cdot t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      times-frac [=>] 1.32	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 1.32	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 1.32	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 1.3	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 1.3	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 1.26

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

   if 4.9999999999999998e-8 < t

   1. Initial program 0.95

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 1.21

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+137}:\\ \;\;\;\;\frac{t}{z \cdot \left(y \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	49.72%
Cost	2036

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ t_2 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-159}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1020000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{+25}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+157}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	50.21%
Cost	2036

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ t_2 := \frac{y}{z \cdot -3}\\ t_3 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-159}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	52.07%
Cost	1772

\[\begin{array}{l} t_1 := t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ t_2 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.1 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 20500000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	49.97%
Cost	1772

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ t_2 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 360000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{+25}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	26.9%
Cost	1505

\[\begin{array}{l} t_1 := t \cdot \frac{0.3333333333333333}{y \cdot z}\\ t_2 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.55 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-252}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-159}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-76} \lor \neg \left(y \leq 2.1 \cdot 10^{-57}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	26.79%
Cost	1504

\[\begin{array}{l} t_1 := t \cdot \frac{0.3333333333333333}{y \cdot z}\\ t_2 := x + \frac{\frac{y}{z}}{-3}\\ t_3 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-251}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-159}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	26.85%
Cost	1504

\[\begin{array}{l} t_1 := \frac{t \cdot 0.3333333333333333}{y \cdot z}\\ t_2 := x + \frac{\frac{y}{z}}{-3}\\ t_3 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-251}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	26.74%
Cost	1504

\[\begin{array}{l} t_1 := x + \frac{\frac{y}{z}}{-3}\\ t_2 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-253}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-159}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-57}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	26.7%
Cost	1504

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ t_2 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-252}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-159}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-57}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	0.85%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+46} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{t}{z \cdot \left(y \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 11
Error	17.72%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-58} \lor \neg \left(x \leq 3.2 \cdot 10^{-78}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \end{array} \]

Alternative 12
Error	12.86%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-17} \lor \neg \left(y \leq 8.6 \cdot 10^{+40}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternative 13
Error	12.9%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-17} \lor \neg \left(y \leq 2.05 \cdot 10^{+40}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 14
Error	5.8%
Cost	704

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

Alternative 15
Error	5.76%
Cost	704

\[x + \frac{y - \frac{t}{y}}{z \cdot -3} \]

Alternative 16
Error	43.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	43.38%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	58.17%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023102 
(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))))