Average Error: 0.1 → 0
Time: 14.0s
Precision: 64
Internal Precision: 576
\[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
↓
\[{d1}^{\left(\left(3 + 2\right) + \left(3 + 2\right)\right)}\]

Error

Bits error versus d1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0
Herbie0
\[{d1}^{10}\]

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. Applied simplify0.1

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

  4. Applied pow20.1

    \[\leadsto \left({d1}^{3} \cdot \left(d1 \cdot d1\right)\right) \cdot \left({d1}^{3} \cdot \color{blue}{{d1}^{2}}\right)\]

  5. Applied pow-prod-up0.1

    \[\leadsto \left({d1}^{3} \cdot \left(d1 \cdot d1\right)\right) \cdot \color{blue}{{d1}^{\left(3 + 2\right)}}\]

  6. Applied pow20.1

    \[\leadsto \left({d1}^{3} \cdot \color{blue}{{d1}^{2}}\right) \cdot {d1}^{\left(3 + 2\right)}\]

  7. Applied pow-prod-up0.1

    \[\leadsto \color{blue}{{d1}^{\left(3 + 2\right)}} \cdot {d1}^{\left(3 + 2\right)}\]

  8. Applied pow-prod-up0

    \[\leadsto \color{blue}{{d1}^{\left(\left(3 + 2\right) + \left(3 + 2\right)\right)}}\]

Runtime

Time bar (total: 14.0s)Debug logProfile

herbie shell --seed '#(1072967564 1937075727 894099792 790700740 1036514779 1027793188)' +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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