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

Average Error: 3.8 → 1.9

Time: 17.1s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+189}:\\ \;\;\;\;t_1 + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-153}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{\frac{t}{y}}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

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+189)
     (+ t_1 (/ (/ t z) (* y 3.0)))
     (if (<= (* z 3.0) 5e-153)
       (+ (- x (/ (/ y z) 3.0)) (/ (/ (/ 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+189) {
		tmp = t_1 + ((t / z) / (y * 3.0));
	} else if ((z * 3.0) <= 5e-153) {
		tmp = (x - ((y / z) / 3.0)) + (((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+189)) then
        tmp = t_1 + ((t / z) / (y * 3.0d0))
    else if ((z * 3.0d0) <= 5d-153) then
        tmp = (x - ((y / z) / 3.0d0)) + (((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+189) {
		tmp = t_1 + ((t / z) / (y * 3.0));
	} else if ((z * 3.0) <= 5e-153) {
		tmp = (x - ((y / z) / 3.0)) + (((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+189:
		tmp = t_1 + ((t / z) / (y * 3.0))
	elif (z * 3.0) <= 5e-153:
		tmp = (x - ((y / z) / 3.0)) + (((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+189)
		tmp = Float64(t_1 + Float64(Float64(t / z) / Float64(y * 3.0)));
	elseif (Float64(z * 3.0) <= 5e-153)
		tmp = Float64(Float64(x - Float64(Float64(y / z) / 3.0)) + Float64(Float64(Float64(t / y) / 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+189)
		tmp = t_1 + ((t / z) / (y * 3.0));
	elseif ((z * 3.0) <= 5e-153)
		tmp = (x - ((y / z) / 3.0)) + (((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+189], N[(t$95$1 + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-153], N[(N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	3.8
Target	1.7
Herbie	1.9

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -5.0000000000000004e189

   1. Initial program 0.7

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

   2. Applied egg-rr 0.6

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\left(t \cdot \frac{\frac{0.3333333333333333}{z}}{y} + 0\right)} \]

   3. Simplified 1.6

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

      [Start] 0.6	\[ \left(x - \frac{y}{z \cdot 3}\right) + \left(t \cdot \frac{\frac{0.3333333333333333}{z}}{y} + 0\right) \]
      rational.json-simplify-4 [=>] 0.6	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]
      rational.json-simplify-44 [=>] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \color{blue}{\frac{\frac{0.3333333333333333}{y}}{z}} \]
      metadata-eval [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{\color{blue}{\frac{1}{3}}}{y}}{z} \]
      rational.json-simplify-46 [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\color{blue}{\frac{1}{3 \cdot y}}}{z} \]
      rational.json-simplify-47 [=>] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \color{blue}{\frac{1}{\left(3 \cdot y\right) \cdot z}} \]
      rational.json-simplify-2 [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{1}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
      rational.json-simplify-5 [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{1}{\color{blue}{z \cdot \left(3 \cdot y\right) - 0}} \]
      rational.json-simplify-50 [=>] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \color{blue}{\frac{-1}{0 - z \cdot \left(3 \cdot y\right)}} \]
      metadata-eval [=>] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\color{blue}{-1}}{0 - z \cdot \left(3 \cdot y\right)} \]
      rational.json-simplify-12 [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{-1}{\color{blue}{-z \cdot \left(3 \cdot y\right)}} \]
      rational.json-simplify-49 [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{-1 \cdot t}{-z \cdot \left(3 \cdot y\right)}} \]
      rational.json-simplify-2 [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{t \cdot -1}}{-z \cdot \left(3 \cdot y\right)} \]
      rational.json-simplify-8 [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{-t}}{-z \cdot \left(3 \cdot y\right)} \]
      rational.json-simplify-12 [=>] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{-t}{\color{blue}{0 - z \cdot \left(3 \cdot y\right)}} \]
      rational.json-simplify-50 [<=] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{z \cdot \left(3 \cdot y\right) - 0}} \]
      rational.json-simplify-5 [=>] 0.7	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
      rational.json-simplify-46 [=>] 1.6	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]
      rational.json-simplify-2 [=>] 1.6	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{\color{blue}{y \cdot 3}} \]

   if -5.0000000000000004e189 < (*.f64 z 3) < 5.00000000000000033e-153

   1. Initial program 7.5

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

   2. Simplified 2.6

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

      [Start] 7.5	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      rational.json-simplify-46 [=>] 7.5	\[ \left(x - \color{blue}{\frac{\frac{y}{z}}{3}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      rational.json-simplify-46 [=>] 1.8	\[ \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]
      rational.json-simplify-44 [=>] 2.6	\[ \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}} \]
      rational.json-simplify-46 [=>] 2.6	\[ \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{\frac{\frac{\frac{t}{y}}{z}}{3}} \]

   if 5.00000000000000033e-153 < (*.f64 z 3)

   1. Initial program 1.3

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

4. Final simplification 1.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+189}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-153}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{\frac{t}{y}}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternatives

Alternative 1
Error	1.0
Cost	1480

\[\begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-153}:\\ \;\;\;\;x + \left(-\frac{-0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	1.7
Cost	1480

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ t_2 := t_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-153}:\\ \;\;\;\;t_1 + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	1.8
Cost	1480

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+185}:\\ \;\;\;\;t_1 + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-153}:\\ \;\;\;\;t_1 + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternative 4
Error	30.8
Cost	1372

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ t_2 := \frac{\frac{y}{-3}}{z}\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-143}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 210000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	29.7
Cost	1372

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ t_2 := \frac{\frac{y}{-3}}{z}\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 190000000:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	29.7
Cost	1372

\[\begin{array}{l} t_1 := \frac{\frac{y}{-3}}{z}\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-254}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 600000000:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	30.5
Cost	1108

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := \frac{\frac{y}{-3}}{z}\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	12.2
Cost	1104

\[\begin{array}{l} t_1 := \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ t_2 := x + \frac{y}{\frac{z}{-0.3333333333333333}}\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 480000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 9
Error	12.1
Cost	1104

\[\begin{array}{l} t_1 := \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{-104}:\\ \;\;\;\;x + \left(-\frac{-0.3333333333333333}{z} \cdot \left(-y\right)\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y}{\frac{z}{-0.3333333333333333}}\\ \mathbf{elif}\;x \leq 190000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 10
Error	8.8
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ t_2 := x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.00305:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\frac{-0.3333333333333333}{z} \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 11
Error	9.3
Cost	1104

\[\begin{array}{l} t_1 := x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00195:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\frac{-0.3333333333333333}{z} \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 12
Error	1.9
Cost	1032

\[\begin{array}{l} t_1 := x + \left(-\frac{-0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-170}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	17.5
Cost	976

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z}{-0.3333333333333333}}\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-91}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-232}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	17.6
Cost	976

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z}{-0.3333333333333333}}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-90}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	28.0
Cost	848

\[\begin{array}{l} t_1 := y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 640000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	28.1
Cost	848

\[\begin{array}{l} t_1 := \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 200000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	28.0
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-95}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 350000000:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	28.1
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-98}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 290000000:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	6.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+36}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 0.029:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\frac{-0.3333333333333333}{z} \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 20
Error	37.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023068 
(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))))