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

Average Error: 3.8 → 0.6

Time: 18.0s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{-24}:\\ \;\;\;\;t_1 + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{elif}\;z \cdot 3 \leq 8 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

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) -5e-24)
     (+ t_1 (/ (/ t (* z 3.0)) y))
     (if (<= (* z 3.0) 8e-27)
       (+ x (/ (- y (/ t y)) (* z -3.0)))
       (+ 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) <= -5e-24) {
		tmp = t_1 + ((t / (z * 3.0)) / y);
	} else if ((z * 3.0) <= 8e-27) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} 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) <= (-5d-24)) then
        tmp = t_1 + ((t / (z * 3.0d0)) / y)
    else if ((z * 3.0d0) <= 8d-27) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    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) <= -5e-24) {
		tmp = t_1 + ((t / (z * 3.0)) / y);
	} else if ((z * 3.0) <= 8e-27) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} 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) <= -5e-24:
		tmp = t_1 + ((t / (z * 3.0)) / y)
	elif (z * 3.0) <= 8e-27:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	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) <= -5e-24)
		tmp = Float64(t_1 + Float64(Float64(t / Float64(z * 3.0)) / y));
	elseif (Float64(z * 3.0) <= 8e-27)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	else
		tmp = Float64(t_1 + Float64(t / Float64(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) <= -5e-24)
		tmp = t_1 + ((t / (z * 3.0)) / y);
	elseif ((z * 3.0) <= 8e-27)
		tmp = x + ((y - (t / y)) / (z * -3.0));
	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], -5e-24], N[(t$95$1 + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 8e-27], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	3.8
Target	1.6
Herbie	0.6

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -4.9999999999999998e-24

   1. Initial program 0.4

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

   2. Simplified 1.1

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

      [Start] 0.4	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-/r* [=>] 1.1	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   if -4.9999999999999998e-24 < (*.f64 z 3) < 8.0000000000000003e-27

   1. Initial program 12.3

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

   2. Simplified 0.3

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

      [Start] 12.3	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 12.3	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 12.3	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 12.3	\[ x + \color{blue}{-1 \cdot \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      distribute-lft-out-- [<=] 12.3	\[ x + \color{blue}{\left(-1 \cdot \frac{y}{z \cdot 3} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      associate-*r/ [=>] 12.3	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*l/ [<=] 12.3	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*r/ [=>] 12.3	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1 \cdot t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      times-frac [=>] 0.3	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 0.3	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 0.3	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 0.3	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 0.3	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 0.3

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

   if 8.0000000000000003e-27 < (*.f64 z 3)

   1. Initial program 0.4

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

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{-24}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{elif}\;z \cdot 3 \leq 8 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.4
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{-24} \lor \neg \left(z \cdot 3 \leq 8 \cdot 10^{-27}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 2
Error	0.4
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{-24} \lor \neg \left(z \cdot 3 \leq 8 \cdot 10^{-27}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 3
Error	17.4
Cost	1372

\[\begin{array}{l} t_1 := \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-160}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-289}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-53}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 4
Error	17.4
Cost	1372

\[\begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{-159}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-252}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-52}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 5
Error	17.4
Cost	1372

\[\begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-159}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-252}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-139}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{\frac{t}{3}}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 6
Error	8.6
Cost	1104

\[\begin{array}{l} t_1 := x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-306}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 38:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 7
Error	8.4
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-308}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.4:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 8
Error	18.4
Cost	976

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ t_2 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	18.4
Cost	976

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 10
Error	18.4
Cost	976

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ t_2 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	18.3
Cost	976

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 12
Error	16.8
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-161}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-139}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-53}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 13
Error	1.9
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-56} \lor \neg \left(y \leq 1.05 \cdot 10^{-57}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

Alternative 14
Error	1.7
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-56} \lor \neg \left(y \leq 10^{-68}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

Alternative 15
Error	1.8
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-56}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1 \cdot -0.3333333333333333}{z}\\ \end{array} \]

Alternative 16
Error	1.8
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t_1}{z}}{-3}\\ \end{array} \]

Alternative 17
Error	9.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 82000:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 18
Error	5.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 62000:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 19
Error	31.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-43}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	37.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022364 
(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))))