Average Error: 3.5 → 1.6
Time: 19.6s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\frac{\frac{t}{3.0} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right)\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\frac{\frac{t}{3.0} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right)
double f(double x, double y, double z, double t) {
        double r38213581 = x;
        double r38213582 = y;
        double r38213583 = z;
        double r38213584 = 3.0;
        double r38213585 = r38213583 * r38213584;
        double r38213586 = r38213582 / r38213585;
        double r38213587 = r38213581 - r38213586;
        double r38213588 = t;
        double r38213589 = r38213585 * r38213582;
        double r38213590 = r38213588 / r38213589;
        double r38213591 = r38213587 + r38213590;
        return r38213591;
}
↓
double f(double x, double y, double z, double t) {
        double r38213592 = t;
        double r38213593 = 3.0;
        double r38213594 = r38213592 / r38213593;
        double r38213595 = 1.0;
        double r38213596 = z;
        double r38213597 = r38213595 / r38213596;
        double r38213598 = r38213594 * r38213597;
        double r38213599 = y;
        double r38213600 = r38213598 / r38213599;
        double r38213601 = x;
        double r38213602 = r38213599 / r38213593;
        double r38213603 = r38213597 * r38213602;
        double r38213604 = r38213601 - r38213603;
        double r38213605 = r38213600 + r38213604;
        return r38213605;
}

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

Original3.5
Target1.6
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]

Derivation

  1. Initial program 3.5

    \[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r*1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3.0}}{y}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.6

    \[\leadsto \left(x - \frac{\color{blue}{1 \cdot y}}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]

  6. Applied times-frac1.6

    \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3.0}}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]
  7. Using strategy rm

  8. Applied *-un-lft-identity1.6

    \[\leadsto \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right) + \frac{\frac{\color{blue}{1 \cdot t}}{z \cdot 3.0}}{y}\]

  9. Applied times-frac1.6

    \[\leadsto \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right) + \frac{\color{blue}{\frac{1}{z} \cdot \frac{t}{3.0}}}{y}\]

  10. Final simplification1.6

    \[\leadsto \frac{\frac{t}{3.0} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))