Average Error: 0.2 → 0.1
Time: 1.7s
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 r883665 = x;
        double r883666 = 3.0;
        double r883667 = r883665 * r883666;
        double r883668 = y;
        double r883669 = r883667 * r883668;
        double r883670 = z;
        double r883671 = r883669 - r883670;
        return r883671;
}
↓
double f(double x, double y, double z) {
        double r883672 = 3.0;
        double r883673 = x;
        double r883674 = y;
        double r883675 = r883673 * r883674;
        double r883676 = r883672 * r883675;
        double r883677 = 1.0;
        double r883678 = pow(r883676, r883677);
        double r883679 = z;
        double r883680 = r883678 - r883679;
        return r883680;
}

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

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

Derivation

  1. Initial program 0.2

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

  3. Applied pow10.2

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

  4. Applied pow10.2

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

  5. Applied pow10.2

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

  6. Applied pow-prod-down0.2

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

  7. Applied pow-prod-down0.2

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

  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 2020065 +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))