Average Error: 4.0 → 1.8
Time: 8.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}
double f(double x, double y, double z, double t) {
        double r700244 = x;
        double r700245 = y;
        double r700246 = z;
        double r700247 = 3.0;
        double r700248 = r700246 * r700247;
        double r700249 = r700245 / r700248;
        double r700250 = r700244 - r700249;
        double r700251 = t;
        double r700252 = r700248 * r700245;
        double r700253 = r700251 / r700252;
        double r700254 = r700250 + r700253;
        return r700254;
}
↓
double f(double x, double y, double z, double t) {
        double r700255 = x;
        double r700256 = 1.0;
        double r700257 = z;
        double r700258 = 3.0;
        double r700259 = r700257 * r700258;
        double r700260 = y;
        double r700261 = r700259 / r700260;
        double r700262 = r700256 / r700261;
        double r700263 = r700255 - r700262;
        double r700264 = t;
        double r700265 = r700264 / r700259;
        double r700266 = r700265 / r700260;
        double r700267 = r700263 + r700266;
        return r700267;
}

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

Original4.0
Target1.7
Herbie1.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 4.0

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

  3. Applied associate-/r*1.7

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

  5. Applied clear-num1.8

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

  6. Final simplification1.8

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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))))