Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Average Error: 0.1 → 0.1

Time: 17.7s

Precision: 64

Math

\[\left(x \cdot 3\right) \cdot y - z\]

↓

\[3 \cdot \left(x \cdot y\right) - z\]

C

double f(double x, double y, double z) {
        double r58156 = x;
        double r58157 = 3.0;
        double r58158 = r58156 * r58157;
        double r58159 = y;
        double r58160 = r58158 * r58159;
        double r58161 = z;
        double r58162 = r58160 - r58161;
        return r58162;
}

↓

double f(double x, double y, double z) {
        double r58163 = 3.0;
        double r58164 = x;
        double r58165 = y;
        double r58166 = r58164 * r58165;
        double r58167 = r58163 * r58166;
        double r58168 = z;
        double r58169 = r58167 - r58168;
        return r58169;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

1. Initial program 0.1

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

3. Applied pow1 0.1

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

4. Applied pow1 0.1

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

5. Applied pow1 0.1

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

6. Applied pow-prod-down 0.1

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

7. Applied pow-prod-down 0.1

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

8. Simplified 0.1

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

9. Final simplification 0.1

   \[\leadsto 3 \cdot \left(x \cdot y\right) - z\]

Reproduce

herbie shell --seed 2019315 +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))