Average Error: 3.4 → 1.5
Time: 4.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}
double f(double x, double y, double z, double t) {
        double r848084 = x;
        double r848085 = y;
        double r848086 = z;
        double r848087 = 3.0;
        double r848088 = r848086 * r848087;
        double r848089 = r848085 / r848088;
        double r848090 = r848084 - r848089;
        double r848091 = t;
        double r848092 = r848088 * r848085;
        double r848093 = r848091 / r848092;
        double r848094 = r848090 + r848093;
        return r848094;
}
↓
double f(double x, double y, double z, double t) {
        double r848095 = x;
        double r848096 = y;
        double r848097 = z;
        double r848098 = r848096 / r848097;
        double r848099 = 3.0;
        double r848100 = r848098 / r848099;
        double r848101 = r848095 - r848100;
        double r848102 = t;
        double r848103 = r848102 / r848097;
        double r848104 = r848103 / r848099;
        double r848105 = r848104 / r848096;
        double r848106 = r848101 + r848105;
        return r848106;
}

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
Target1.5
Herbie1.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.4

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

  3. Applied associate-/r*1.5

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

  5. Applied associate-/r*1.5

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

  7. Applied associate-/r*1.5

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

  8. Final simplification1.5

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

Reproduce

herbie shell --seed 2020065 
(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))))