FastMath test5

Average Error: 0.1 → 0

Time: 47.8s

Precision: 64

Math

\[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]

↓

\[{d1}^{10}\]

C

double f(double d1) {
        double r45592027 = d1;
        double r45592028 = r45592027 * r45592027;
        double r45592029 = r45592027 * r45592028;
        double r45592030 = r45592029 * r45592027;
        double r45592031 = r45592030 * r45592027;
        double r45592032 = r45592031 * r45592028;
        double r45592033 = r45592032 * r45592027;
        double r45592034 = r45592027 * r45592033;
        double r45592035 = r45592034 * r45592027;
        return r45592035;
}

↓

double f(double d1) {
        double r45592036 = d1;
        double r45592037 = 10.0;
        double r45592038 = pow(r45592036, r45592037);
        return r45592038;
}

Error

Bits error versus d1

Target

Original	0.1
Target	0
Herbie	0

\[{d1}^{10}\]

Derivation

1. Initial program 0.1

   \[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
2. Using strategy rm

3. Applied pow1 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot \color{blue}{{d1}^{1}}\right)\right) \cdot d1\]

4. Applied pow2 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \color{blue}{{d1}^{2}}\right) \cdot {d1}^{1}\right)\right) \cdot d1\]

5. Applied pow2 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \color{blue}{{d1}^{2}}\right) \cdot d1\right) \cdot d1\right) \cdot {d1}^{2}\right) \cdot {d1}^{1}\right)\right) \cdot d1\]

6. Applied pow1 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\left(\color{blue}{{d1}^{1}} \cdot {d1}^{2}\right) \cdot d1\right) \cdot d1\right) \cdot {d1}^{2}\right) \cdot {d1}^{1}\right)\right) \cdot d1\]

7. Applied pow-prod-up 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\color{blue}{{d1}^{\left(1 + 2\right)}} \cdot d1\right) \cdot d1\right) \cdot {d1}^{2}\right) \cdot {d1}^{1}\right)\right) \cdot d1\]

8. Applied pow-plus 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\color{blue}{{d1}^{\left(\left(1 + 2\right) + 1\right)}} \cdot d1\right) \cdot {d1}^{2}\right) \cdot {d1}^{1}\right)\right) \cdot d1\]

9. Applied pow-plus 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\color{blue}{{d1}^{\left(\left(\left(1 + 2\right) + 1\right) + 1\right)}} \cdot {d1}^{2}\right) \cdot {d1}^{1}\right)\right) \cdot d1\]

10. Applied pow-prod-up 0.1

    \[\leadsto \left(d1 \cdot \left(\color{blue}{{d1}^{\left(\left(\left(\left(1 + 2\right) + 1\right) + 1\right) + 2\right)}} \cdot {d1}^{1}\right)\right) \cdot d1\]

11. Applied pow-prod-up 0.1

    \[\leadsto \left(d1 \cdot \color{blue}{{d1}^{\left(\left(\left(\left(\left(1 + 2\right) + 1\right) + 1\right) + 2\right) + 1\right)}}\right) \cdot d1\]

12. Simplified 0.1

    \[\leadsto \left(d1 \cdot {d1}^{\color{blue}{8}}\right) \cdot d1\]

13. Taylor expanded around 0 0

    \[\leadsto \color{blue}{{d1}^{10}}\]

14. Final simplification 0

    \[\leadsto {d1}^{10}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

  (* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1))