Average Error: 3.7 → 1.8
Time: 3.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{\frac{t}{z \cdot 3}}}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{\frac{t}{z \cdot 3}}}
double f(double x, double y, double z, double t) {
        double r904604 = x;
        double r904605 = y;
        double r904606 = z;
        double r904607 = 3.0;
        double r904608 = r904606 * r904607;
        double r904609 = r904605 / r904608;
        double r904610 = r904604 - r904609;
        double r904611 = t;
        double r904612 = r904608 * r904605;
        double r904613 = r904611 / r904612;
        double r904614 = r904610 + r904613;
        return r904614;
}
↓
double f(double x, double y, double z, double t) {
        double r904615 = x;
        double r904616 = y;
        double r904617 = z;
        double r904618 = r904616 / r904617;
        double r904619 = 3.0;
        double r904620 = r904618 / r904619;
        double r904621 = r904615 - r904620;
        double r904622 = 1.0;
        double r904623 = t;
        double r904624 = r904617 * r904619;
        double r904625 = r904623 / r904624;
        double r904626 = r904616 / r904625;
        double r904627 = r904622 / r904626;
        double r904628 = r904621 + r904627;
        return r904628;
}

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
Herbie1.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

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*1.8

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

  5. Applied associate-/r*1.8

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

  7. Applied clear-num1.8

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{\frac{1}{\frac{y}{\frac{t}{z \cdot 3}}}}\]

  8. Final simplification1.8

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{\frac{t}{z \cdot 3}}}\]

Reproduce

herbie shell --seed 2020060 
(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))))