Average Error: 3.7 → 1.6
Time: 6.6s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z}}{3} \cdot \frac{1}{y}\]
\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{\frac{t}{z}}{3} \cdot \frac{1}{y}
double f(double x, double y, double z, double t) {
        double r754240 = x;
        double r754241 = y;
        double r754242 = z;
        double r754243 = 3.0;
        double r754244 = r754242 * r754243;
        double r754245 = r754241 / r754244;
        double r754246 = r754240 - r754245;
        double r754247 = t;
        double r754248 = r754244 * r754241;
        double r754249 = r754247 / r754248;
        double r754250 = r754246 + r754249;
        return r754250;
}
↓
double f(double x, double y, double z, double t) {
        double r754251 = x;
        double r754252 = y;
        double r754253 = z;
        double r754254 = r754252 / r754253;
        double r754255 = 3.0;
        double r754256 = r754254 / r754255;
        double r754257 = r754251 - r754256;
        double r754258 = t;
        double r754259 = r754258 / r754253;
        double r754260 = r754259 / r754255;
        double r754261 = 1.0;
        double r754262 = r754261 / r754252;
        double r754263 = r754260 * r754262;
        double r754264 = r754257 + r754263;
        return r754264;
}

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
Target1.6
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

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*1.6

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

  5. Applied div-inv1.7

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

  7. Applied associate-/r*1.7

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

  9. Applied associate-/r*1.6

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

  10. Final simplification1.6

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

Reproduce

herbie shell --seed 2020042 
(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))))