Average Error: 3.7 → 1.5
Time: 4.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z \cdot 3} \cdot \frac{\sqrt[3]{t}}{y}\]
\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{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z \cdot 3} \cdot \frac{\sqrt[3]{t}}{y}
double f(double x, double y, double z, double t) {
        double r773361 = x;
        double r773362 = y;
        double r773363 = z;
        double r773364 = 3.0;
        double r773365 = r773363 * r773364;
        double r773366 = r773362 / r773365;
        double r773367 = r773361 - r773366;
        double r773368 = t;
        double r773369 = r773365 * r773362;
        double r773370 = r773368 / r773369;
        double r773371 = r773367 + r773370;
        return r773371;
}
↓
double f(double x, double y, double z, double t) {
        double r773372 = x;
        double r773373 = y;
        double r773374 = z;
        double r773375 = 3.0;
        double r773376 = r773374 * r773375;
        double r773377 = r773373 / r773376;
        double r773378 = r773372 - r773377;
        double r773379 = t;
        double r773380 = cbrt(r773379);
        double r773381 = r773380 * r773380;
        double r773382 = r773381 / r773376;
        double r773383 = r773380 / r773373;
        double r773384 = r773382 * r773383;
        double r773385 = r773378 + r773384;
        return r773385;
}

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
Target1.9
Herbie1.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

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 add-cube-cbrt3.9

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

  4. Applied times-frac1.5

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

  5. Final simplification1.5

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

Reproduce

herbie shell --seed 2020062 
(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))))