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

Average Accuracy: 94.2% → 98.4%

Time: 15.2s

Precision: binary64

Cost: 3016

Math

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

↓

\[\begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ t_2 := y - \frac{t}{y}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\frac{t_2}{z}}{-3}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+269}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_2}{z \cdot -3}\\ \end{array} \]

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))) (/ t (* y (* z 3.0)))))
        (t_2 (- y (/ t y))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (/ t_2 z) -3.0))
     (if (<= t_1 4e+269) t_1 (+ x (/ t_2 (* 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))) + (t / (y * (z * 3.0)));
	double t_2 = y - (t / y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((t_2 / z) / -3.0);
	} else if (t_1 <= 4e+269) {
		tmp = t_1;
	} else {
		tmp = x + (t_2 / (z * -3.0));
	}
	return tmp;
}

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))) + (t / (y * (z * 3.0)));
	double t_2 = y - (t / y);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((t_2 / z) / -3.0);
	} else if (t_1 <= 4e+269) {
		tmp = t_1;
	} else {
		tmp = x + (t_2 / (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))) + (t / (y * (z * 3.0)))
	t_2 = y - (t / y)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((t_2 / z) / -3.0)
	elif t_1 <= 4e+269:
		tmp = t_1
	else:
		tmp = x + (t_2 / (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(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))))
	t_2 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(t_2 / z) / -3.0));
	elseif (t_1 <= 4e+269)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t_2 / 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))) + (t / (y * (z * 3.0)));
	t_2 = y - (t / y);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((t_2 / z) / -3.0);
	elseif (t_1 <= 4e+269)
		tmp = t_1;
	else
		tmp = x + (t_2 / (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[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(t$95$2 / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+269], t$95$1, N[(x + N[(t$95$2 / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	94.2%
Target	97.4%
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 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < -inf.0

   1. Initial program 0.0%

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

   2. Simplified 99.4%

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

      [Start] 0.0	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 0.0	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 0.0	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 0.0	\[ x + \color{blue}{-1 \cdot \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      distribute-lft-out-- [<=] 0.0	\[ x + \color{blue}{\left(-1 \cdot \frac{y}{z \cdot 3} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      associate-*r/ [=>] 0.0	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*l/ [<=] 0.0	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*r/ [=>] 0.0	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1 \cdot t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      times-frac [=>] 99.5	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 99.4	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 99.4	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 99.4	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 99.4	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 99.1%

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

   if -inf.0 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < 4.0000000000000002e269

   1. Initial program 99.1%

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

   if 4.0000000000000002e269 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))

   1. Initial program 70.6%

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

   2. Simplified 91.4%

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

      [Start] 70.6	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 70.6	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 70.6	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 70.6	\[ x + \color{blue}{-1 \cdot \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      distribute-lft-out-- [<=] 70.6	\[ x + \color{blue}{\left(-1 \cdot \frac{y}{z \cdot 3} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      associate-*r/ [=>] 70.6	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*l/ [<=] 70.5	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*r/ [=>] 70.5	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1 \cdot t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      times-frac [=>] 91.4	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 91.4	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 91.4	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 91.4	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 91.4	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 91.5%

      \[\leadsto x + \color{blue}{\frac{y - \frac{t}{y}}{z \cdot -3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq -\infty:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \mathbf{elif}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 4 \cdot 10^{+269}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	50.0%
Cost	1640

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-222}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 2
Accuracy	50.2%
Cost	1508

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-285}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 3
Accuracy	50.1%
Cost	1508

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := 0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 4
Accuracy	70.1%
Cost	1372

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := x + y \cdot \frac{-0.3333333333333333}{z}\\ t_3 := 0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-285}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	70.1%
Cost	1372

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := x + y \cdot \frac{-0.3333333333333333}{z}\\ t_3 := 0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-287}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	70.1%
Cost	1372

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ t_2 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_3 := x + \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-221}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Accuracy	72.8%
Cost	976

\[\begin{array}{l} t_1 := x + \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-78}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-221}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	72.8%
Cost	976

\[\begin{array}{l} t_1 := x + \frac{\frac{y}{z}}{-3}\\ \mathbf{if}\;y \leq -7 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;\frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-221}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-136}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	96.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-29} \lor \neg \left(y \leq 1.35 \cdot 10^{-60}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y} \cdot \frac{t}{z \cdot 3}\\ \end{array} \]

Alternative 10
Accuracy	96.8%
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{1}{y} \cdot \frac{t}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 11
Accuracy	96.8%
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{1}{y} \cdot \frac{t}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t_1}{z}}{-3}\\ \end{array} \]

Alternative 12
Accuracy	93.7%
Cost	964

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 10^{+241}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \end{array} \]

Alternative 13
Accuracy	86.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+27} \lor \neg \left(y \leq 3.85 \cdot 10^{-28}\right):\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \end{array} \]

Alternative 14
Accuracy	86.5%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+33} \lor \neg \left(y \leq 2.65 \cdot 10^{-31}\right):\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternative 15
Accuracy	80.4%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-109}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 16
Accuracy	80.1%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{-117}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{t}{y} - y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 17
Accuracy	55.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	55.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Accuracy	40.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023129 
(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))))