FastMath test5

Average Error: 0.1 → 0

Time: 13.0s

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 r8615071 = d1;
        double r8615072 = r8615071 * r8615071;
        double r8615073 = r8615071 * r8615072;
        double r8615074 = r8615073 * r8615071;
        double r8615075 = r8615074 * r8615071;
        double r8615076 = r8615075 * r8615072;
        double r8615077 = r8615076 * r8615071;
        double r8615078 = r8615071 * r8615077;
        double r8615079 = r8615078 * r8615071;
        return r8615079;
}

↓

double f(double d1) {
        double r8615080 = d1;
        double r8615081 = 10.0;
        double r8615082 = pow(r8615080, r8615081);
        return r8615082;
}

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. Simplified 0.2

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

4. Applied pow2 0.2

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

5. Applied pow1 0.2

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

6. Applied pow1 0.2

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

7. Applied pow-prod-up 0.2

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

8. Applied pow1 0.2

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

9. Applied pow-prod-up 0.2

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

10. Applied pow-prod-up 0.1

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

11. Simplified 0.1

    \[\leadsto {d1}^{\color{blue}{5}} \cdot \left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot \left(d1 \cdot d1\right)\right)\]
12. Using strategy rm

13. Applied pow2 0.1

    \[\leadsto {d1}^{5} \cdot \left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot \color{blue}{{d1}^{2}}\right)\]

14. Applied pow1 0.1

    \[\leadsto {d1}^{5} \cdot \left(\left(d1 \cdot \left(\color{blue}{{d1}^{1}} \cdot d1\right)\right) \cdot {d1}^{2}\right)\]

15. Applied pow-plus 0.1

    \[\leadsto {d1}^{5} \cdot \left(\left(d1 \cdot \color{blue}{{d1}^{\left(1 + 1\right)}}\right) \cdot {d1}^{2}\right)\]

16. Applied pow1 0.1

    \[\leadsto {d1}^{5} \cdot \left(\left(\color{blue}{{d1}^{1}} \cdot {d1}^{\left(1 + 1\right)}\right) \cdot {d1}^{2}\right)\]

17. Applied pow-prod-up 0.1

    \[\leadsto {d1}^{5} \cdot \left(\color{blue}{{d1}^{\left(1 + \left(1 + 1\right)\right)}} \cdot {d1}^{2}\right)\]

18. Applied pow-prod-up 0.1

    \[\leadsto {d1}^{5} \cdot \color{blue}{{d1}^{\left(\left(1 + \left(1 + 1\right)\right) + 2\right)}}\]

19. Applied pow-prod-up 0

    \[\leadsto \color{blue}{{d1}^{\left(5 + \left(\left(1 + \left(1 + 1\right)\right) + 2\right)\right)}}\]

20. Simplified 0

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

21. Final simplification 0

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

Reproduce

herbie shell --seed 2019135 
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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