Average Error: 0.1 → 0.1
Time: 1.8s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[{\left(3 \cdot \left(x \cdot y\right)\right)}^{1} - z\]
\left(x \cdot 3\right) \cdot y - z
↓
{\left(3 \cdot \left(x \cdot y\right)\right)}^{1} - z
double f(double x, double y, double z) {
        double r689334 = x;
        double r689335 = 3.0;
        double r689336 = r689334 * r689335;
        double r689337 = y;
        double r689338 = r689336 * r689337;
        double r689339 = z;
        double r689340 = r689338 - r689339;
        return r689340;
}
↓
double f(double x, double y, double z) {
        double r689341 = 3.0;
        double r689342 = x;
        double r689343 = y;
        double r689344 = r689342 * r689343;
        double r689345 = r689341 * r689344;
        double r689346 = 1.0;
        double r689347 = pow(r689345, r689346);
        double r689348 = z;
        double r689349 = r689347 - r689348;
        return r689349;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.2
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

  1. Initial program 0.1

    \[\left(x \cdot 3\right) \cdot y - z\]
  2. Using strategy rm

  3. Applied pow10.1

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

  4. Applied pow10.1

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

  5. Applied pow10.1

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

  6. Applied pow-prod-down0.1

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

  7. Applied pow-prod-down0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3 y)) z)

  (- (* (* x 3) y) z))