Average Error: 3.7 → 1.0
Time: 4.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{\sqrt[3]{y}}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{\sqrt[3]{y}}
double f(double x, double y, double z, double t) {
        double r853246 = x;
        double r853247 = y;
        double r853248 = z;
        double r853249 = 3.0;
        double r853250 = r853248 * r853249;
        double r853251 = r853247 / r853250;
        double r853252 = r853246 - r853251;
        double r853253 = t;
        double r853254 = r853250 * r853247;
        double r853255 = r853253 / r853254;
        double r853256 = r853252 + r853255;
        return r853256;
}
↓
double f(double x, double y, double z, double t) {
        double r853257 = x;
        double r853258 = y;
        double r853259 = z;
        double r853260 = 3.0;
        double r853261 = r853259 * r853260;
        double r853262 = r853258 / r853261;
        double r853263 = r853257 - r853262;
        double r853264 = t;
        double r853265 = cbrt(r853264);
        double r853266 = r853265 * r853265;
        double r853267 = r853266 / r853259;
        double r853268 = cbrt(r853258);
        double r853269 = r853268 * r853268;
        double r853270 = r853267 / r853269;
        double r853271 = r853265 / r853260;
        double r853272 = r853271 / r853268;
        double r853273 = r853270 * r853272;
        double r853274 = r853263 + r853273;
        return r853274;
}

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
Target1.7
Herbie1.0
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.7

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

  3. Applied associate-/r*1.7

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

  5. Applied add-cube-cbrt2.0

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

  6. Applied add-cube-cbrt2.0

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

  7. Applied times-frac2.0

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

  8. Applied times-frac1.0

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

  9. Final simplification1.0

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))