FastMath test5

Average Error: 0.1 → 0

Time: 11.9s

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 r4082165 = d1;
        double r4082166 = r4082165 * r4082165;
        double r4082167 = r4082165 * r4082166;
        double r4082168 = r4082167 * r4082165;
        double r4082169 = r4082168 * r4082165;
        double r4082170 = r4082169 * r4082166;
        double r4082171 = r4082170 * r4082165;
        double r4082172 = r4082165 * r4082171;
        double r4082173 = r4082172 * r4082165;
        return r4082173;
}

↓

double f(double d1) {
        double r4082174 = d1;
        double r4082175 = 10.0;
        double r4082176 = pow(r4082174, r4082175);
        return r4082176;
}

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 pow2 0.1

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

4. Applied pow1 0.1

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

5. Applied pow1 0.1

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

6. Applied pow1 0.1

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

7. Applied pow-sqr 0.1

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

8. Applied pow1 0.1

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

9. Applied pow-prod-up 0.1

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

10. Applied pow-plus 0.1

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

11. Applied pow-prod-up 0.1

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

12. Applied pow-prod-up 0.1

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

13. Simplified 0.1

    \[\leadsto \left(d1 \cdot \left({d1}^{\color{blue}{7}} \cdot d1\right)\right) \cdot d1\]
14. Using strategy rm

15. Applied pow1 0.1

    \[\leadsto \left(d1 \cdot \left({d1}^{7} \cdot \color{blue}{{d1}^{1}}\right)\right) \cdot d1\]

16. Applied pow-prod-up 0.1

    \[\leadsto \left(d1 \cdot \color{blue}{{d1}^{\left(7 + 1\right)}}\right) \cdot d1\]

17. Applied pow1 0.1

    \[\leadsto \left(\color{blue}{{d1}^{1}} \cdot {d1}^{\left(7 + 1\right)}\right) \cdot d1\]

18. Applied pow-prod-up 0.0

    \[\leadsto \color{blue}{{d1}^{\left(1 + \left(7 + 1\right)\right)}} \cdot d1\]

19. Applied pow-plus 0

    \[\leadsto \color{blue}{{d1}^{\left(\left(1 + \left(7 + 1\right)\right) + 1\right)}}\]

20. Simplified 0

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

21. Final simplification 0

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

Reproduce

herbie shell --seed 2019151 
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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