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

Average Accuracy: 94.2% → 98.4%

Time: 16.3s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{-119}:\\ \;\;\;\;t_1 + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 3 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{3}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1 + t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \]

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) -5e-119)
     (+ t_1 (/ t (* y (* z 3.0))))
     (if (<= (* z 3.0) 3e+137)
       (+ x (/ (/ (- (/ t y) y) 3.0) z))
       (+ t_1 (* t (/ (/ 0.3333333333333333 y) z)))))))

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) <= -5e-119) {
		tmp = t_1 + (t / (y * (z * 3.0)));
	} else if ((z * 3.0) <= 3e+137) {
		tmp = x + ((((t / y) - y) / 3.0) / z);
	} else {
		tmp = t_1 + (t * ((0.3333333333333333 / y) / z));
	}
	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) <= (-5d-119)) then
        tmp = t_1 + (t / (y * (z * 3.0d0)))
    else if ((z * 3.0d0) <= 3d+137) then
        tmp = x + ((((t / y) - y) / 3.0d0) / z)
    else
        tmp = t_1 + (t * ((0.3333333333333333d0 / y) / z))
    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) <= -5e-119) {
		tmp = t_1 + (t / (y * (z * 3.0)));
	} else if ((z * 3.0) <= 3e+137) {
		tmp = x + ((((t / y) - y) / 3.0) / z);
	} else {
		tmp = t_1 + (t * ((0.3333333333333333 / y) / z));
	}
	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) <= -5e-119:
		tmp = t_1 + (t / (y * (z * 3.0)))
	elif (z * 3.0) <= 3e+137:
		tmp = x + ((((t / y) - y) / 3.0) / z)
	else:
		tmp = t_1 + (t * ((0.3333333333333333 / y) / z))
	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) <= -5e-119)
		tmp = Float64(t_1 + Float64(t / Float64(y * Float64(z * 3.0))));
	elseif (Float64(z * 3.0) <= 3e+137)
		tmp = Float64(x + Float64(Float64(Float64(Float64(t / y) - y) / 3.0) / z));
	else
		tmp = Float64(t_1 + Float64(t * Float64(Float64(0.3333333333333333 / y) / z)));
	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) <= -5e-119)
		tmp = t_1 + (t / (y * (z * 3.0)));
	elseif ((z * 3.0) <= 3e+137)
		tmp = x + ((((t / y) - y) / 3.0) / z);
	else
		tmp = t_1 + (t * ((0.3333333333333333 / y) / z));
	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], -5e-119], N[(t$95$1 + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 3e+137], N[(x + N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	94.2%
Target	97.5%
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) < -4.99999999999999993e-119

   1. Initial program 98.5%

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

   if -4.99999999999999993e-119 < (*.f64 z 3) < 3.0000000000000001e137

   1. Initial program 86.5%

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

   2. Simplified 97.6%

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

      [Start] 86.5	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 86.5	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 86.5	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      sub-neg [=>] 86.5	\[ x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]
      distribute-neg-in [=>] 86.5	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      unsub-neg [=>] 86.5	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 86.5	\[ x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*r/ [=>] 86.5	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*l/ [<=] 86.4	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      distribute-neg-frac [=>] 86.4	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      neg-mul-1 [=>] 86.4	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]
      times-frac [=>] 97.6	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 97.6	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 97.6	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 97.6	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 97.6	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Taylor expanded in z around 0 97.5%

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

   4. Simplified 97.7%

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

      [Start] 97.5	\[ x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z} \]
      metadata-eval [<=] 97.5	\[ x + \color{blue}{\frac{0.3333333333333333}{-1}} \cdot \frac{y - \frac{t}{y}}{z} \]
      times-frac [<=] 97.6	\[ x + \color{blue}{\frac{0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}{-1 \cdot z}} \]
      metadata-eval [<=] 97.6	\[ x + \frac{\color{blue}{\left(--0.3333333333333333\right)} \cdot \left(y - \frac{t}{y}\right)}{-1 \cdot z} \]
      distribute-lft-neg-in [<=] 97.6	\[ x + \frac{\color{blue}{--0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}}{-1 \cdot z} \]
      associate-/r* [=>] 97.6	\[ x + \color{blue}{\frac{\frac{--0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}{-1}}{z}} \]
      *-commutative [=>] 97.6	\[ x + \frac{\frac{-\color{blue}{\left(y - \frac{t}{y}\right) \cdot -0.3333333333333333}}{-1}}{z} \]
      distribute-lft-neg-in [=>] 97.6	\[ x + \frac{\frac{\color{blue}{\left(-\left(y - \frac{t}{y}\right)\right) \cdot -0.3333333333333333}}{-1}}{z} \]
      associate-/l* [=>] 97.7	\[ x + \frac{\color{blue}{\frac{-\left(y - \frac{t}{y}\right)}{\frac{-1}{-0.3333333333333333}}}}{z} \]
      neg-sub0 [=>] 97.7	\[ x + \frac{\frac{\color{blue}{0 - \left(y - \frac{t}{y}\right)}}{\frac{-1}{-0.3333333333333333}}}{z} \]
      sub-neg [=>] 97.7	\[ x + \frac{\frac{0 - \color{blue}{\left(y + \left(-\frac{t}{y}\right)\right)}}{\frac{-1}{-0.3333333333333333}}}{z} \]
      distribute-frac-neg [<=] 97.7	\[ x + \frac{\frac{0 - \left(y + \color{blue}{\frac{-t}{y}}\right)}{\frac{-1}{-0.3333333333333333}}}{z} \]
      +-commutative [=>] 97.7	\[ x + \frac{\frac{0 - \color{blue}{\left(\frac{-t}{y} + y\right)}}{\frac{-1}{-0.3333333333333333}}}{z} \]
      associate--r+ [=>] 97.7	\[ x + \frac{\frac{\color{blue}{\left(0 - \frac{-t}{y}\right) - y}}{\frac{-1}{-0.3333333333333333}}}{z} \]
      neg-sub0 [<=] 97.7	\[ x + \frac{\frac{\color{blue}{\left(-\frac{-t}{y}\right)} - y}{\frac{-1}{-0.3333333333333333}}}{z} \]
      distribute-frac-neg [=>] 97.7	\[ x + \frac{\frac{\left(-\color{blue}{\left(-\frac{t}{y}\right)}\right) - y}{\frac{-1}{-0.3333333333333333}}}{z} \]
      remove-double-neg [=>] 97.7	\[ x + \frac{\frac{\color{blue}{\frac{t}{y}} - y}{\frac{-1}{-0.3333333333333333}}}{z} \]
      metadata-eval [=>] 97.7	\[ x + \frac{\frac{\frac{t}{y} - y}{\color{blue}{3}}}{z} \]

   if 3.0000000000000001e137 < (*.f64 z 3)

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 99.4%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]

   3. Simplified 99.5%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{y}}{z}} \]
      Proof

      [Start] 99.4	\[ \left(x - \frac{y}{z \cdot 3}\right) + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]
      associate-*r/ [=>] 99.4	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{0.3333333333333333 \cdot t}{y \cdot z}} \]
      *-commutative [=>] 99.4	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{t \cdot 0.3333333333333333}}{y \cdot z} \]
      *-commutative [=>] 99.4	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t \cdot 0.3333333333333333}{\color{blue}{z \cdot y}} \]
      associate-*r/ [<=] 99.4	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{t \cdot \frac{0.3333333333333333}{z \cdot y}} \]
      *-commutative [<=] 99.4	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{0.3333333333333333}{\color{blue}{y \cdot z}} \]
      associate-/r* [=>] 99.5	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \color{blue}{\frac{\frac{0.3333333333333333}{y}}{z}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{-119}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 3 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{3}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.3%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{-119} \lor \neg \left(z \cdot 3 \leq 3 \cdot 10^{+137}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{3}}{z}\\ \end{array} \]

Alternative 2
Accuracy	74.2%
Cost	977

\[\begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-215} \lor \neg \left(y \leq 1.6 \cdot 10^{-125}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]

Alternative 3
Accuracy	74.2%
Cost	976

\[\begin{array}{l} t_1 := x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -6 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-215}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-125}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	74.4%
Cost	976

\[\begin{array}{l} t_1 := x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-215}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-125}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	74.4%
Cost	976

\[\begin{array}{l} t_1 := x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-93}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-207}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-125}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	86.4%
Cost	972

\[\begin{array}{l} t_1 := x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -1.62 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-300}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-31}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	96.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-110} \lor \neg \left(y \leq 9.2 \cdot 10^{-33}\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \]

Alternative 8
Accuracy	97.0%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-109} \lor \neg \left(y \leq 9.2 \cdot 10^{-33}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \]

Alternative 9
Accuracy	97.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-109} \lor \neg \left(y \leq 9.2 \cdot 10^{-33}\right):\\ \;\;\;\;x + \frac{\frac{\frac{t}{y} - y}{3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \]

Alternative 10
Accuracy	97.5%
Cost	960

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

Alternative 11
Accuracy	56.4%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-86}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;x \leq 6.8:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	56.3%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-68}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{elif}\;x \leq 0.033:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	85.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-41} \lor \neg \left(y \leq 1.55 \cdot 10^{-28}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]

Alternative 14
Accuracy	91.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{-40} \lor \neg \left(y \leq 4 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \]

Alternative 15
Accuracy	56.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Accuracy	56.6%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 72:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Accuracy	42.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(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))))