Average Error: 3.6 → 1.7
Time: 6.2s
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 r841485 = x;
        double r841486 = y;
        double r841487 = z;
        double r841488 = 3.0;
        double r841489 = r841487 * r841488;
        double r841490 = r841486 / r841489;
        double r841491 = r841485 - r841490;
        double r841492 = t;
        double r841493 = r841489 * r841486;
        double r841494 = r841492 / r841493;
        double r841495 = r841491 + r841494;
        return r841495;
}
↓
double f(double x, double y, double z, double t) {
        double r841496 = x;
        double r841497 = y;
        double r841498 = z;
        double r841499 = 3.0;
        double r841500 = r841498 * r841499;
        double r841501 = r841497 / r841500;
        double r841502 = r841496 - r841501;
        double r841503 = t;
        double r841504 = cbrt(r841503);
        double r841505 = r841504 * r841504;
        double r841506 = r841505 / r841500;
        double r841507 = r841504 / r841497;
        double r841508 = r841506 * r841507;
        double r841509 = r841502 + r841508;
        return r841509;
}

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

Derivation

  1. Initial program 3.6

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

  3. Applied add-cube-cbrt3.8

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

  4. Applied times-frac1.7

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

  5. Final simplification1.7

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

Reproduce

herbie shell --seed 2020046 
(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))))