Average Error: 3.9 → 1.7
Time: 15.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\frac{\frac{\frac{t}{z}}{3}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\frac{\frac{\frac{t}{z}}{3}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)
double f(double x, double y, double z, double t) {
        double r32848266 = x;
        double r32848267 = y;
        double r32848268 = z;
        double r32848269 = 3.0;
        double r32848270 = r32848268 * r32848269;
        double r32848271 = r32848267 / r32848270;
        double r32848272 = r32848266 - r32848271;
        double r32848273 = t;
        double r32848274 = r32848270 * r32848267;
        double r32848275 = r32848273 / r32848274;
        double r32848276 = r32848272 + r32848275;
        return r32848276;
}
↓
double f(double x, double y, double z, double t) {
        double r32848277 = t;
        double r32848278 = z;
        double r32848279 = r32848277 / r32848278;
        double r32848280 = 3.0;
        double r32848281 = r32848279 / r32848280;
        double r32848282 = y;
        double r32848283 = r32848281 / r32848282;
        double r32848284 = x;
        double r32848285 = 1.0;
        double r32848286 = r32848285 / r32848278;
        double r32848287 = r32848282 / r32848280;
        double r32848288 = r32848286 * r32848287;
        double r32848289 = r32848284 - r32848288;
        double r32848290 = r32848283 + r32848289;
        return r32848290;
}

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

Original3.9
Target1.7
Herbie1.7
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.9

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  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 associate-/r*1.7

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

  7. Applied *-un-lft-identity1.7

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

  8. Applied times-frac1.7

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

  9. Final simplification1.7

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

Reproduce

herbie shell --seed 2019192 
(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))))