Average Error: 3.6 → 1.8
Time: 10.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}\]
\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{\frac{\frac{t}{z}}{3}}{y}
double f(double x, double y, double z, double t) {
        double r500471 = x;
        double r500472 = y;
        double r500473 = z;
        double r500474 = 3.0;
        double r500475 = r500473 * r500474;
        double r500476 = r500472 / r500475;
        double r500477 = r500471 - r500476;
        double r500478 = t;
        double r500479 = r500475 * r500472;
        double r500480 = r500478 / r500479;
        double r500481 = r500477 + r500480;
        return r500481;
}
↓
double f(double x, double y, double z, double t) {
        double r500482 = x;
        double r500483 = y;
        double r500484 = z;
        double r500485 = 3.0;
        double r500486 = r500484 * r500485;
        double r500487 = r500483 / r500486;
        double r500488 = r500482 - r500487;
        double r500489 = t;
        double r500490 = r500489 / r500484;
        double r500491 = r500490 / r500485;
        double r500492 = r500491 / r500483;
        double r500493 = r500488 + r500492;
        return r500493;
}

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
Target1.8
Herbie1.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

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 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

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

  6. Final simplification1.8

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

Reproduce

herbie shell --seed 2019303 
(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))))