Average Error: 3.4 → 1.6
Time: 11.6s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\frac{\frac{t}{z}}{y \cdot 3.0} + \left(x - \frac{\frac{y}{z}}{3.0}\right)\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\frac{\frac{t}{z}}{y \cdot 3.0} + \left(x - \frac{\frac{y}{z}}{3.0}\right)
double f(double x, double y, double z, double t) {
        double r15063665 = x;
        double r15063666 = y;
        double r15063667 = z;
        double r15063668 = 3.0;
        double r15063669 = r15063667 * r15063668;
        double r15063670 = r15063666 / r15063669;
        double r15063671 = r15063665 - r15063670;
        double r15063672 = t;
        double r15063673 = r15063669 * r15063666;
        double r15063674 = r15063672 / r15063673;
        double r15063675 = r15063671 + r15063674;
        return r15063675;
}
↓
double f(double x, double y, double z, double t) {
        double r15063676 = t;
        double r15063677 = z;
        double r15063678 = r15063676 / r15063677;
        double r15063679 = y;
        double r15063680 = 3.0;
        double r15063681 = r15063679 * r15063680;
        double r15063682 = r15063678 / r15063681;
        double r15063683 = x;
        double r15063684 = r15063679 / r15063677;
        double r15063685 = r15063684 / r15063680;
        double r15063686 = r15063683 - r15063685;
        double r15063687 = r15063682 + r15063686;
        return r15063687;
}

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

Original3.4
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 3.4

    \[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
  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 associate-/r*1.6

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

  7. Applied associate-/r*1.6

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

  9. Applied div-inv1.6

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

  10. Applied associate-/l*1.6

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

  11. Simplified1.6

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

  12. Final simplification1.6

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

Reproduce

herbie shell --seed 2019156 
(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))))