Average Error: 3.7 → 1.6
Time: 3.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{0.333333333333333315 \cdot \frac{t}{z}}}\]
\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{1}{\frac{y}{0.333333333333333315 \cdot \frac{t}{z}}}
double f(double x, double y, double z, double t) {
        double r726205 = x;
        double r726206 = y;
        double r726207 = z;
        double r726208 = 3.0;
        double r726209 = r726207 * r726208;
        double r726210 = r726206 / r726209;
        double r726211 = r726205 - r726210;
        double r726212 = t;
        double r726213 = r726209 * r726206;
        double r726214 = r726212 / r726213;
        double r726215 = r726211 + r726214;
        return r726215;
}
↓
double f(double x, double y, double z, double t) {
        double r726216 = x;
        double r726217 = y;
        double r726218 = z;
        double r726219 = r726217 / r726218;
        double r726220 = 3.0;
        double r726221 = r726219 / r726220;
        double r726222 = r726216 - r726221;
        double r726223 = 1.0;
        double r726224 = 0.3333333333333333;
        double r726225 = t;
        double r726226 = r726225 / r726218;
        double r726227 = r726224 * r726226;
        double r726228 = r726217 / r726227;
        double r726229 = r726223 / r726228;
        double r726230 = r726222 + r726229;
        return r726230;
}

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

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

Derivation

  1. Initial program 3.7

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

  3. Applied associate-/r*1.6

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

  4. Taylor expanded around 0 1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{0.333333333333333315 \cdot \frac{t}{z}}}{y}\]
  5. Using strategy rm

  6. Applied associate-/r*1.6

    \[\leadsto \left(x - \color{blue}{\frac{\frac{y}{z}}{3}}\right) + \frac{0.333333333333333315 \cdot \frac{t}{z}}{y}\]
  7. Using strategy rm

  8. Applied clear-num1.6

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{\frac{1}{\frac{y}{0.333333333333333315 \cdot \frac{t}{z}}}}\]

  9. Final simplification1.6

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{0.333333333333333315 \cdot \frac{t}{z}}}\]

Reproduce

herbie shell --seed 2020024 +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))))