Average Error: 3.7 → 0.4
Time: 13.8s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -1.153736389036113 \cdot 10^{-20} \lor \neg \left(t \leq 9.039394313155043 \cdot 10^{-52}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y - \frac{t}{y}}}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -1.153736389036113 \cdot 10^{-20} \lor \neg \left(t \leq 9.039394313155043 \cdot 10^{-52}\right):\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y - \frac{t}{y}}}\\

\end{array}
(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 (or (<= t -1.153736389036113e-20) (not (<= t 9.039394313155043e-52)))
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
   (+ x (/ -0.3333333333333333 (/ z (- y (/ t y)))))))
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 <= -1.153736389036113e-20) || !(t <= 9.039394313155043e-52)) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + (-0.3333333333333333 / (z / (y - (t / y))));
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target1.8
Herbie0.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.153736389036113e-20 or 9.03939431315504343e-52 < t

    1. Initial program 0.6

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

    if -1.153736389036113e-20 < t < 9.03939431315504343e-52

    1. Initial program 6.7

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

    2. Simplified0.2

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

    4. Applied associate-*l/_binary64_208220.2

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

    6. Applied associate-/l*_binary64_208240.2

      \[\leadsto x + \color{blue}{\frac{-0.3333333333333333}{\frac{z}{y - \frac{t}{y}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.153736389036113 \cdot 10^{-20} \lor \neg \left(t \leq 9.039394313155043 \cdot 10^{-52}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y - \frac{t}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021007 
(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))))