Average Error: 3.6 → 0.7
Time: 7.1s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.20900859555046478 \cdot 10^{76} \lor \neg \left(t \le 3.4334795866523095 \cdot 10^{-75}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.20900859555046478 \cdot 10^{76} \lor \neg \left(t \le 3.4334795866523095 \cdot 10^{-75}\right):\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - ((double) (y / ((double) (z * 3.0)))))) + ((double) (t / ((double) (((double) (z * 3.0)) * y))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((t <= -2.2090085955504648e+76) || !(t <= 3.4334795866523095e-75))) {
		VAR = ((double) (((double) (x - ((double) (y / ((double) (z * 3.0)))))) + ((double) (0.3333333333333333 * ((double) (t / ((double) (z * y))))))));
	} else {
		VAR = ((double) (((double) (x - ((double) (((double) (y / z)) / 3.0)))) + ((double) (((double) (t / y)) / ((double) (z * 3.0))))));
	}
	return VAR;
}

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

Original3.6
Target1.8
Herbie0.7
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.20900859555046478e76 or 3.4334795866523095e-75 < t

    1. Initial program 1.0

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

    2. Taylor expanded around 0 1.0

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{0.333333333333333315 \cdot \frac{t}{z \cdot y}}\]

    if -2.20900859555046478e76 < t < 3.4334795866523095e-75

    1. Initial program 5.5

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

    3. Applied add-cube-cbrt5.6

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

    4. Applied times-frac0.9

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

    6. Applied associate-*l/0.6

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

    7. Simplified0.4

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

    9. Applied associate-/r*0.4

      \[\leadsto \left(x - \color{blue}{\frac{\frac{y}{z}}{3}}\right) + \frac{\frac{t}{y}}{z \cdot 3}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.20900859555046478 \cdot 10^{76} \lor \neg \left(t \le 3.4334795866523095 \cdot 10^{-75}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \end{array}\]

Reproduce

herbie shell --seed 2020173 
(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))))