Average Error: 3.6 → 1.6
Time: 3.1s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \left(0.333333333333333315 \cdot \frac{t}{z}\right) \cdot \frac{1}{y}\]
\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) + \left(0.333333333333333315 \cdot \frac{t}{z}\right) \cdot \frac{1}{y}
double f(double x, double y, double z, double t) {
        double r759325 = x;
        double r759326 = y;
        double r759327 = z;
        double r759328 = 3.0;
        double r759329 = r759327 * r759328;
        double r759330 = r759326 / r759329;
        double r759331 = r759325 - r759330;
        double r759332 = t;
        double r759333 = r759329 * r759326;
        double r759334 = r759332 / r759333;
        double r759335 = r759331 + r759334;
        return r759335;
}
↓
double f(double x, double y, double z, double t) {
        double r759336 = x;
        double r759337 = y;
        double r759338 = z;
        double r759339 = r759337 / r759338;
        double r759340 = 3.0;
        double r759341 = r759339 / r759340;
        double r759342 = r759336 - r759341;
        double r759343 = 0.3333333333333333;
        double r759344 = t;
        double r759345 = r759344 / r759338;
        double r759346 = r759343 * r759345;
        double r759347 = 1.0;
        double r759348 = r759347 / r759337;
        double r759349 = r759346 * r759348;
        double r759350 = r759342 + r759349;
        return r759350;
}

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

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*1.6

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

  5. Applied associate-/r*1.6

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

  6. Taylor expanded around 0 1.6

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\color{blue}{0.333333333333333315 \cdot \frac{t}{z}}}{y}\]
  7. Using strategy rm

  8. Applied div-inv1.6

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{\left(0.333333333333333315 \cdot \frac{t}{z}\right) \cdot \frac{1}{y}}\]

  9. Final simplification1.6

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \left(0.333333333333333315 \cdot \frac{t}{z}\right) \cdot \frac{1}{y}\]

Reproduce

herbie shell --seed 2020049 
(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))))