Average Error: 3.7 → 1.8
Time: 5.0s
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 r852245 = x;
        double r852246 = y;
        double r852247 = z;
        double r852248 = 3.0;
        double r852249 = r852247 * r852248;
        double r852250 = r852246 / r852249;
        double r852251 = r852245 - r852250;
        double r852252 = t;
        double r852253 = r852249 * r852246;
        double r852254 = r852252 / r852253;
        double r852255 = r852251 + r852254;
        return r852255;
}
↓
double f(double x, double y, double z, double t) {
        double r852256 = x;
        double r852257 = y;
        double r852258 = z;
        double r852259 = r852257 / r852258;
        double r852260 = 3.0;
        double r852261 = r852259 / r852260;
        double r852262 = r852256 - r852261;
        double r852263 = 1.0;
        double r852264 = t;
        double r852265 = r852258 * r852260;
        double r852266 = r852264 / r852265;
        double r852267 = r852257 / r852266;
        double r852268 = r852263 / r852267;
        double r852269 = r852262 + r852268;
        return r852269;
}

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))))