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

Average Accuracy: 94.5% → 98.5%

Time: 18.4s

Precision: binary64

Cost: 7496

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+65}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{\frac{\frac{t}{z}}{y}}{3}\right)\\ \end{array} \]

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
 (if (<= t -5e+65)
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
   (if (<= t 1.1e-103)
     (+ x (/ (- y (/ t y)) (* z -3.0)))
     (+ x (fma -0.3333333333333333 (/ y z) (/ (/ (/ t z) y) 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 tmp;
	if (t <= -5e+65) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else if (t <= 1.1e-103) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = x + fma(-0.3333333333333333, (y / z), (((t / z) / y) / 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)
	tmp = 0.0
	if (t <= -5e+65)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))));
	elseif (t <= 1.1e-103)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	else
		tmp = Float64(x + fma(-0.3333333333333333, Float64(y / z), Float64(Float64(Float64(t / z) / y) / 3.0)));
	end
	return 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_] := If[LessEqual[t, -5e+65], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-103], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + N[(N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	94.5%
Target	97.0%
Herbie	98.5%

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

Derivation

1. Split input into 3 regimes

2. if t < -4.99999999999999973e65

   1. Initial program 99.0%

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

   if -4.99999999999999973e65 < t < 1.1e-103

   1. Initial program 91.2%

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

   2. Simplified 99.4%

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

      [Start] 91.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 91.2	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 91.2	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      sub-neg [=>] 91.2	\[ x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]
      distribute-neg-in [=>] 91.2	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      unsub-neg [=>] 91.2	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 91.2	\[ x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*r/ [=>] 91.2	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*l/ [<=] 91.1	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      distribute-neg-frac [=>] 91.1	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      neg-mul-1 [=>] 91.1	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]
      times-frac [=>] 99.4	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 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 99.4%

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

      [Start] 99.4	\[ x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right) \]
      *-commutative [=>] 99.4	\[ x + \color{blue}{\left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}} \]
      clear-num [=>] 99.3	\[ x + \left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \]
      un-div-inv [=>] 99.4	\[ x + \color{blue}{\frac{y - \frac{t}{y}}{\frac{z}{-0.3333333333333333}}} \]
      div-inv [=>] 99.4	\[ x + \frac{y - \frac{t}{y}}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}} \]
      metadata-eval [=>] 99.4	\[ x + \frac{y - \frac{t}{y}}{z \cdot \color{blue}{-3}} \]

   if 1.1e-103 < t

   1. Initial program 97.8%

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

   2. Simplified 96.5%

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

      [Start] 97.8	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 97.8	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 97.8	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      sub-neg [=>] 97.8	\[ x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]
      distribute-neg-in [=>] 97.8	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      distribute-neg-frac [=>] 97.8	\[ x + \left(\color{blue}{\frac{-y}{z \cdot 3}} + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right) \]
      neg-mul-1 [=>] 97.8	\[ x + \left(\frac{\color{blue}{-1 \cdot y}}{z \cdot 3} + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right) \]
      *-commutative [=>] 97.8	\[ x + \left(\frac{-1 \cdot y}{\color{blue}{3 \cdot z}} + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right) \]
      times-frac [=>] 97.7	\[ x + \left(\color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right) \]
      remove-double-neg [=>] 97.7	\[ x + \left(\frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      fma-def [=>] 97.7	\[ x + \color{blue}{\mathsf{fma}\left(\frac{-1}{3}, \frac{y}{z}, \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      metadata-eval [=>] 97.7	\[ x + \mathsf{fma}\left(\color{blue}{-0.3333333333333333}, \frac{y}{z}, \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*l* [=>] 97.7	\[ x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}}\right) \]
      associate-/r* [=>] 96.6	\[ x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}}\right) \]
      associate-/l/ [<=] 96.5	\[ x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \color{blue}{\frac{\frac{\frac{t}{z}}{y}}{3}}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+65}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{\frac{\frac{t}{z}}{y}}{3}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	67.3%
Cost	2009

\[\begin{array}{l} t_1 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot 3 \leq -4 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{-94}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 8 \cdot 10^{+71} \lor \neg \left(z \cdot 3 \leq 10^{+115}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \]

Alternative 2
Accuracy	75.2%
Cost	1618

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+64} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-55} \lor \neg \left(z \cdot 3 \leq 4 \cdot 10^{+56}\right) \land z \cdot 3 \leq 10^{+115}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]

Alternative 3
Accuracy	75.3%
Cost	1617

\[\begin{array}{l} t_1 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{-55}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{+56} \lor \neg \left(z \cdot 3 \leq 10^{+115}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]

Alternative 4
Accuracy	53.1%
Cost	1376

\[\begin{array}{l} t_1 := \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-140}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-176}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Accuracy	53.6%
Cost	1376

\[\begin{array}{l} t_1 := \frac{y \cdot -0.3333333333333333}{z}\\ t_2 := \frac{\frac{t}{z}}{y} \cdot 0.3333333333333333\\ \mathbf{if}\;x \leq -1.26 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	67.4%
Cost	1241

\[\begin{array}{l} t_1 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{t}{z}}{y} \cdot 0.3333333333333333\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-94}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+71} \lor \neg \left(z \leq 2.5 \cdot 10^{+114}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 7
Accuracy	67.3%
Cost	1241

\[\begin{array}{l} t_1 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{t}{z}}{y} \cdot 0.3333333333333333\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-94}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+71} \lor \neg \left(z \leq 2.5 \cdot 10^{+114}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \]

Alternative 8
Accuracy	98.3%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+63}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-186}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\frac{t}{z}}{y \cdot 3} + \frac{-0.3333333333333333}{\frac{z}{y}}\right)\\ \end{array} \]

Alternative 9
Accuracy	52.3%
Cost	1112

\[\begin{array}{l} t_1 := \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{if}\;x \leq -1.26 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-176}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Accuracy	86.8%
Cost	972

\[\begin{array}{l} t_1 := x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-291}:\\ \;\;\;\;x + \frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	93.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-177} \lor \neg \left(y \leq -3.8 \cdot 10^{-293}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 12
Accuracy	94.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-176} \lor \neg \left(y \leq 6.5 \cdot 10^{-301}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 13
Accuracy	96.9%
Cost	960

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

Alternative 14
Accuracy	52.9%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-11} \lor \neg \left(x \leq -3.2 \cdot 10^{-143}\right) \land x \leq 6.5 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Accuracy	52.9%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-13} \lor \neg \left(x \leq -3.2 \cdot 10^{-143}\right) \land x \leq 7.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Accuracy	52.8%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -0.0017:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-67}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Accuracy	52.8%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -0.00049:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq -1.04 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	85.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-44} \lor \neg \left(y \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \]

Alternative 19
Accuracy	86.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-50} \lor \neg \left(y \leq 5 \cdot 10^{+26}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 20
Accuracy	41.4%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023147 
(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))))