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

Average Accuracy: 94.3% → 98.6%

Time: 18.5s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;t_1 + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

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) -2e+43)
     (+ t_1 (/ (* (/ t z) 0.3333333333333333) y))
     (if (<= (* z 3.0) 5e-31)
       (+ 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) <= -2e+43) {
		tmp = t_1 + (((t / z) * 0.3333333333333333) / y);
	} else if ((z * 3.0) <= 5e-31) {
		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) <= (-2d+43)) then
        tmp = t_1 + (((t / z) * 0.3333333333333333d0) / y)
    else if ((z * 3.0d0) <= 5d-31) 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) <= -2e+43) {
		tmp = t_1 + (((t / z) * 0.3333333333333333) / y);
	} else if ((z * 3.0) <= 5e-31) {
		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) <= -2e+43:
		tmp = t_1 + (((t / z) * 0.3333333333333333) / y)
	elif (z * 3.0) <= 5e-31:
		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) <= -2e+43)
		tmp = Float64(t_1 + Float64(Float64(Float64(t / z) * 0.3333333333333333) / y));
	elseif (Float64(z * 3.0) <= 5e-31)
		tmp = Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / z) / -3.0));
	else
		tmp = Float64(t_1 + Float64(Float64(t / 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) <= -2e+43)
		tmp = t_1 + (((t / z) * 0.3333333333333333) / y);
	elseif ((z * 3.0) <= 5e-31)
		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], -2e+43], N[(t$95$1 + N[(N[(N[(t / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-31], N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	94.3%
Target	97.5%
Herbie	98.6%

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -2.00000000000000003e43

   1. Initial program 99.0%

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

   2. Simplified 98.2%

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

      [Start] 99.0	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-/r* [=>] 98.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   3. Applied egg-rr 98.2%

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

      [Start] 98.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \]
      associate-/r* [=>] 98.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]
      div-inv [=>] 98.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{t}{z} \cdot \frac{1}{3}}}{y} \]
      metadata-eval [=>] 98.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z} \cdot \color{blue}{0.3333333333333333}}{y} \]

   if -2.00000000000000003e43 < (*.f64 z 3) < 5e-31

   1. Initial program 85.2%

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

   2. Simplified 99.3%

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

      [Start] 85.2	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 85.2	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 85.2	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 85.2	\[ x + \color{blue}{-1 \cdot \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      distribute-lft-out-- [<=] 85.2	\[ x + \color{blue}{\left(-1 \cdot \frac{y}{z \cdot 3} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      associate-*r/ [=>] 85.2	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*l/ [<=] 85.2	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*r/ [=>] 85.2	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1 \cdot t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      times-frac [=>] 99.3	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 99.3	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 99.3	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 99.3	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 99.3	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 99.2%

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

      [Start] 99.3	\[ x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right) \]
      *-commutative [=>] 99.3	\[ x + \color{blue}{\left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}} \]
      associate-*r/ [=>] 99.3	\[ x + \color{blue}{\frac{\left(y - \frac{t}{y}\right) \cdot -0.3333333333333333}{z}} \]
      associate-/l* [=>] 99.3	\[ x + \color{blue}{\frac{y - \frac{t}{y}}{\frac{z}{-0.3333333333333333}}} \]
      div-inv [=>] 99.4	\[ x + \frac{y - \frac{t}{y}}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}} \]
      associate-/r* [=>] 99.2	\[ x + \color{blue}{\frac{\frac{y - \frac{t}{y}}{z}}{\frac{1}{-0.3333333333333333}}} \]
      metadata-eval [=>] 99.2	\[ x + \frac{\frac{y - \frac{t}{y}}{z}}{\color{blue}{-3}} \]

   if 5e-31 < (*.f64 z 3)

   1. Initial program 99.3%

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

   2. Simplified 98.3%

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

      [Start] 99.3	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-/r* [=>] 98.3	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.2%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+34} \lor \neg \left(z \cdot 3 \leq 10^{-32}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \end{array} \]

Alternative 2
Accuracy	98.6%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+43} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+14}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \end{array} \]

Alternative 3
Accuracy	99.2%
Cost	1480

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+34}:\\ \;\;\;\;t_1 + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternative 4
Accuracy	53.9%
Cost	1372

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{if}\;x \leq -800:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-282}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-127}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Accuracy	67.6%
Cost	1243

\[\begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+161} \lor \neg \left(t \leq -2.6 \cdot 10^{+109}\right) \land \left(t \leq 10^{-111} \lor \neg \left(t \leq 1.9 \cdot 10^{-86} \lor \neg \left(t \leq 1.7 \cdot 10^{+80}\right) \land t \leq 4.2 \cdot 10^{+252}\right)\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]

Alternative 6
Accuracy	67.8%
Cost	1241

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ t_2 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-86} \lor \neg \left(t \leq 1.7 \cdot 10^{+80}\right) \land t \leq 5 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 7
Accuracy	67.7%
Cost	1240

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ t_2 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+79}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+252}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 8
Accuracy	67.7%
Cost	1240

\[\begin{array}{l} t_1 := \frac{t}{z \cdot \left(3 \cdot y\right)}\\ t_2 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+80}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+252}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 9
Accuracy	67.9%
Cost	1240

\[\begin{array}{l} t_1 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;t \leq -1.38 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;t \leq 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-86}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \frac{t}{y}}{z}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+80}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+252}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 10
Accuracy	67.9%
Cost	1240

\[\begin{array}{l} t_1 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;t \leq 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-86}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \frac{t}{y}}{z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+252}:\\ \;\;\;\;\frac{\frac{t}{3}}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 11
Accuracy	67.9%
Cost	1240

\[\begin{array}{l} t_1 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+109}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;t \leq 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{t}{y}}{\frac{z}{0.3333333333333333}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+80}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+251}:\\ \;\;\;\;\frac{\frac{t}{3}}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \end{array} \]

Alternative 12
Accuracy	97.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-52} \lor \neg \left(y \leq 2.6 \cdot 10^{-98}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

Alternative 13
Accuracy	97.3%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-67} \lor \neg \left(y \leq 4.5 \cdot 10^{-105}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \end{array} \]

Alternative 14
Accuracy	97.4%
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{\frac{t_1}{z}}{-3}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \end{array} \]

Alternative 15
Accuracy	85.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -550000000 \lor \neg \left(y \leq 0.000106\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]

Alternative 16
Accuracy	87.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -124 \lor \neg \left(y \leq 2.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \]

Alternative 17
Accuracy	90.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -580000 \lor \neg \left(y \leq 4.1 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \end{array} \]

Alternative 18
Accuracy	90.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -290000000000 \lor \neg \left(y \leq 8.2 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

Alternative 19
Accuracy	56.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -20000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-47}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Accuracy	56.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -15000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Accuracy	56.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -5400:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-49}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Accuracy	56.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -18000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Accuracy	40.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023133 
(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))))