FastMath test5

Average Error: 0.1 → 0

Time: 40.7s

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 r10804867 = d1;
        double r10804868 = r10804867 * r10804867;
        double r10804869 = r10804867 * r10804868;
        double r10804870 = r10804869 * r10804867;
        double r10804871 = r10804870 * r10804867;
        double r10804872 = r10804871 * r10804868;
        double r10804873 = r10804872 * r10804867;
        double r10804874 = r10804867 * r10804873;
        double r10804875 = r10804874 * r10804867;
        return r10804875;
}

↓

double f(double d1) {
        double r10804876 = d1;
        double r10804877 = 10.0;
        double r10804878 = pow(r10804876, r10804877);
        return r10804878;
}

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

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

4. Applied pow-plus 0.1

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

5. Applied pow1 0.1

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

6. Applied cube-unmult 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\color{blue}{{d1}^{3}} \cdot d1\right) \cdot {d1}^{1}\right) \cdot {d1}^{\left(1 + 1\right)}\right) \cdot d1\right)\right) \cdot d1\]

7. Applied pow-plus 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\color{blue}{{d1}^{\left(3 + 1\right)}} \cdot {d1}^{1}\right) \cdot {d1}^{\left(1 + 1\right)}\right) \cdot d1\right)\right) \cdot d1\]

8. Applied pow-prod-up 0.1

   \[\leadsto \left(d1 \cdot \left(\left(\color{blue}{{d1}^{\left(\left(3 + 1\right) + 1\right)}} \cdot {d1}^{\left(1 + 1\right)}\right) \cdot d1\right)\right) \cdot d1\]

9. Applied pow-prod-up 0.1

   \[\leadsto \left(d1 \cdot \left(\color{blue}{{d1}^{\left(\left(\left(3 + 1\right) + 1\right) + \left(1 + 1\right)\right)}} \cdot d1\right)\right) \cdot d1\]

10. Applied pow-plus 0.1

    \[\leadsto \left(d1 \cdot \color{blue}{{d1}^{\left(\left(\left(\left(3 + 1\right) + 1\right) + \left(1 + 1\right)\right) + 1\right)}}\right) \cdot d1\]

11. Applied pow1 0.1

    \[\leadsto \left(\color{blue}{{d1}^{1}} \cdot {d1}^{\left(\left(\left(\left(3 + 1\right) + 1\right) + \left(1 + 1\right)\right) + 1\right)}\right) \cdot d1\]

12. Applied pow-prod-up 0.0

    \[\leadsto \color{blue}{{d1}^{\left(1 + \left(\left(\left(\left(3 + 1\right) + 1\right) + \left(1 + 1\right)\right) + 1\right)\right)}} \cdot d1\]

13. Applied pow-plus 0

    \[\leadsto \color{blue}{{d1}^{\left(\left(1 + \left(\left(\left(\left(3 + 1\right) + 1\right) + \left(1 + 1\right)\right) + 1\right)\right) + 1\right)}}\]

14. Simplified 0

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

15. Final simplification 0

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

Reproduce

herbie shell --seed 2019149 
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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