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

Percentage Accurate: 95.5% → 97.8%

Time: 8.5s

Precision: binary64

Cost: 968

• 28.0% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \end{array} \]

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 (<= y -5e-55)
   (+ x (/ (- y (/ t y)) (* z -3.0)))
   (if (<= y 1.05e-188)
     (+ x (/ (/ (* t 0.3333333333333333) z) y))
     (+ x (/ (* 0.3333333333333333 (- (/ t y) y)) z)))))

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 (y <= -5e-55) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else if (y <= 1.05e-188) {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	} else {
		tmp = x + ((0.3333333333333333 * ((t / y) - y)) / z);
	}
	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) :: tmp
    if (y <= (-5d-55)) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    else if (y <= 1.05d-188) then
        tmp = x + (((t * 0.3333333333333333d0) / z) / y)
    else
        tmp = x + ((0.3333333333333333d0 * ((t / y) - y)) / z)
    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 tmp;
	if (y <= -5e-55) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else if (y <= 1.05e-188) {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	} else {
		tmp = x + ((0.3333333333333333 * ((t / y) - y)) / z);
	}
	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):
	tmp = 0
	if y <= -5e-55:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	elif y <= 1.05e-188:
		tmp = x + (((t * 0.3333333333333333) / z) / y)
	else:
		tmp = x + ((0.3333333333333333 * ((t / y) - y)) / z)
	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 (y <= -5e-55)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	elseif (y <= 1.05e-188)
		tmp = Float64(x + Float64(Float64(Float64(t * 0.3333333333333333) / z) / y));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * Float64(Float64(t / y) - y)) / z));
	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)
	tmp = 0.0;
	if (y <= -5e-55)
		tmp = x + ((y - (t / y)) / (z * -3.0));
	elseif (y <= 1.05e-188)
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	else
		tmp = x + ((0.3333333333333333 * ((t / y) - y)) / z);
	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_] := If[LessEqual[y, -5e-55], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-188], N[(x + N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Target

Original	95.5%
Target	96.2%
Herbie	97.8%

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

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000002e-55

   1. Initial program 95.9%

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

   2. Simplified 99.7%

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

      [Start] 95.9%	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 95.9%	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 95.9%	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      sub-neg [=>] 95.9%	\[ x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]
      distribute-neg-in [=>] 95.9%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      unsub-neg [=>] 95.9%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 95.9%	\[ x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*r/ [=>] 95.9%	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*l/ [<=] 95.7%	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      distribute-neg-frac [=>] 95.7%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      neg-mul-1 [=>] 95.7%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]
      times-frac [=>] 97.0%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 99.7%	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 99.7%	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 99.7%	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 99.7%	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
      Step-by-step derivation

      [Start] 99.7%	\[ x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right) \]
      clear-num [=>] 99.7%	\[ x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]
      inv-pow [=>] 99.7%	\[ x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]

   4. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]
      Step-by-step derivation

      [Start] 99.7%	\[ x + {\left(\frac{z}{-0.3333333333333333}\right)}^{-1} \cdot \left(y - \frac{t}{y}\right) \]
      unpow-1 [=>] 99.7%	\[ x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]

   5. Applied egg-rr 99.8%

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

      [Start] 99.7%	\[ x + \frac{1}{\frac{z}{-0.3333333333333333}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-*l/ [=>] 99.7%	\[ x + \color{blue}{\frac{1 \cdot \left(y - \frac{t}{y}\right)}{\frac{z}{-0.3333333333333333}}} \]
      *-un-lft-identity [<=] 99.7%	\[ x + \frac{\color{blue}{y - \frac{t}{y}}}{\frac{z}{-0.3333333333333333}} \]
      div-inv [=>] 99.8%	\[ x + \frac{y - \frac{t}{y}}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}} \]
      metadata-eval [=>] 99.8%	\[ x + \frac{y - \frac{t}{y}}{z \cdot \color{blue}{-3}} \]

   if -5.0000000000000002e-55 < y < 1.05e-188

   1. Initial program 93.1%

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

   2. Simplified 83.4%

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

      [Start] 93.1%	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 93.1%	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 93.1%	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      sub-neg [=>] 93.1%	\[ x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]
      distribute-neg-in [=>] 93.1%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      unsub-neg [=>] 93.1%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 93.1%	\[ x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*r/ [=>] 93.1%	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*l/ [<=] 93.1%	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      distribute-neg-frac [=>] 93.1%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      neg-mul-1 [=>] 93.1%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]
      times-frac [=>] 83.5%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 83.5%	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 83.5%	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 83.4%	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 83.4%	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Taylor expanded in y around 0 93.0%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]

   4. Simplified 83.4%

      \[\leadsto x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]
      Step-by-step derivation

      [Start] 93.0%	\[ x + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]
      *-commutative [=>] 93.0%	\[ x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]
      associate-*l/ [=>] 93.0%	\[ x + \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]
      times-frac [=>] 83.4%	\[ x + \color{blue}{\frac{t}{y} \cdot \frac{0.3333333333333333}{z}} \]

   5. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]
      Step-by-step derivation

      [Start] 83.4%	\[ x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z} \]
      associate-*l/ [=>] 98.9%	\[ x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   6. Applied egg-rr 99.0%

      \[\leadsto x + \frac{\color{blue}{\frac{t \cdot 0.3333333333333333}{z}}}{y} \]
      Step-by-step derivation

      [Start] 98.9%	\[ x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y} \]
      associate-*r/ [=>] 99.0%	\[ x + \frac{\color{blue}{\frac{t \cdot 0.3333333333333333}{z}}}{y} \]

   if 1.05e-188 < y

   1. Initial program 97.8%

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

   2. Simplified 99.7%

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

      [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%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      unsub-neg [=>] 97.8%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 97.8%	\[ x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*r/ [=>] 97.8%	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*l/ [<=] 97.7%	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      distribute-neg-frac [=>] 97.7%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      neg-mul-1 [=>] 97.7%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]
      times-frac [=>] 99.6%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 99.7%	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 99.7%	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 99.7%	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 99.7%	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Taylor expanded in y around 0 97.8%

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

   4. Simplified 99.8%

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

      [Start] 97.8%	\[ x + \left(-0.3333333333333333 \cdot \frac{y}{z} + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\right) \]
      +-commutative [=>] 97.8%	\[ x + \color{blue}{\left(0.3333333333333333 \cdot \frac{t}{y \cdot z} + -0.3333333333333333 \cdot \frac{y}{z}\right)} \]
      metadata-eval [<=] 97.8%	\[ x + \left(0.3333333333333333 \cdot \frac{t}{y \cdot z} + \color{blue}{\left(-0.3333333333333333\right)} \cdot \frac{y}{z}\right) \]
      cancel-sign-sub-inv [<=] 97.8%	\[ x + \color{blue}{\left(0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z}\right)} \]
      associate-/r* [=>] 99.7%	\[ x + \left(0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{y}}{z}} - 0.3333333333333333 \cdot \frac{y}{z}\right) \]
      associate-*r/ [=>] 99.8%	\[ x + \left(\color{blue}{\frac{0.3333333333333333 \cdot \frac{t}{y}}{z}} - 0.3333333333333333 \cdot \frac{y}{z}\right) \]
      associate-*r/ [=>] 99.8%	\[ x + \left(\frac{0.3333333333333333 \cdot \frac{t}{y}}{z} - \color{blue}{\frac{0.3333333333333333 \cdot y}{z}}\right) \]
      div-sub [<=] 99.8%	\[ x + \color{blue}{\frac{0.3333333333333333 \cdot \frac{t}{y} - 0.3333333333333333 \cdot y}{z}} \]
      distribute-lft-out-- [=>] 99.8%	\[ x + \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]

3. Recombined 3 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	97.8%
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \end{array} \]

Alternative 2
Accuracy	97.4%
Cost	1988

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;t_1 + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 10^{+282}:\\ \;\;\;\;t_1 + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \]

Alternative 3
Accuracy	97.5%
Cost	1988

\[\begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t_1 \leq 10^{+282}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \]

Alternative 4
Accuracy	98.0%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-54} \lor \neg \left(y \leq 1.5 \cdot 10^{-148}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 5
Accuracy	97.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-54} \lor \neg \left(y \leq 5.8 \cdot 10^{-189}\right):\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 6
Accuracy	89.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+39} \lor \neg \left(y \leq 9.5 \cdot 10^{+22}\right):\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 7
Accuracy	89.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+41} \lor \neg \left(y \leq 3.4 \cdot 10^{+22}\right):\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \end{array} \]

Alternative 8
Accuracy	92.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+40} \lor \neg \left(y \leq 7000000000\right):\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \end{array} \]

Alternative 9
Accuracy	92.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+39} \lor \neg \left(y \leq 20000\right):\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 10
Accuracy	65.1%
Cost	448

\[x + y \cdot \frac{-0.3333333333333333}{z} \]

Alternative 11
Accuracy	65.1%
Cost	448

\[x + \frac{y}{z \cdot -3} \]

Alternative 12
Accuracy	65.1%
Cost	448

\[x + \frac{\frac{y}{-3}}{z} \]

Alternative 13
Accuracy	30.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023171 
(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))))