Average Error: 3.7 → 1.8
Time: 4.2s
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 r813021 = x;
        double r813022 = y;
        double r813023 = z;
        double r813024 = 3.0;
        double r813025 = r813023 * r813024;
        double r813026 = r813022 / r813025;
        double r813027 = r813021 - r813026;
        double r813028 = t;
        double r813029 = r813025 * r813022;
        double r813030 = r813028 / r813029;
        double r813031 = r813027 + r813030;
        return r813031;
}
↓
double f(double x, double y, double z, double t) {
        double r813032 = x;
        double r813033 = y;
        double r813034 = z;
        double r813035 = r813033 / r813034;
        double r813036 = 3.0;
        double r813037 = r813035 / r813036;
        double r813038 = r813032 - r813037;
        double r813039 = 1.0;
        double r813040 = t;
        double r813041 = r813034 * r813036;
        double r813042 = r813040 / r813041;
        double r813043 = r813033 / r813042;
        double r813044 = r813039 / r813043;
        double r813045 = r813038 + r813044;
        return r813045;
}

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 +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))))