Average Error: 3.5 → 1.6
Time: 15.6s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\frac{\frac{\frac{t}{z}}{3}}{y} + \left(x - \frac{\frac{y}{3}}{z}\right)\]
\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{\frac{y}{3}}{z}\right)
double f(double x, double y, double z, double t) {
        double r578539 = x;
        double r578540 = y;
        double r578541 = z;
        double r578542 = 3.0;
        double r578543 = r578541 * r578542;
        double r578544 = r578540 / r578543;
        double r578545 = r578539 - r578544;
        double r578546 = t;
        double r578547 = r578543 * r578540;
        double r578548 = r578546 / r578547;
        double r578549 = r578545 + r578548;
        return r578549;
}
↓
double f(double x, double y, double z, double t) {
        double r578550 = t;
        double r578551 = z;
        double r578552 = r578550 / r578551;
        double r578553 = 3.0;
        double r578554 = r578552 / r578553;
        double r578555 = y;
        double r578556 = r578554 / r578555;
        double r578557 = x;
        double r578558 = r578555 / r578553;
        double r578559 = r578558 / r578551;
        double r578560 = r578557 - r578559;
        double r578561 = r578556 + r578560;
        return r578561;
}

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

Original3.5
Target1.7
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.5

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  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. Simplified1.6

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

  6. Applied *-un-lft-identity1.6

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

  7. Applied times-frac1.7

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

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

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

  10. Applied associate-*l*1.7

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

  11. Simplified1.6

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

  12. Final simplification1.6

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

Reproduce

herbie shell --seed 2019194 
(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))))