Average Error: 0.1 → 0
Time: 12.8s
Precision: 64
Internal Precision: 576
\[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
\[{d1}^{\left(9 + 1\right)}\]

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. Using strategy rm
  3. Applied cube-unmult0.1

    \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\color{blue}{{d1}^{3}} \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
  4. Applied pow-plus0.1

    \[\leadsto \left(d1 \cdot \left(\left(\left(\color{blue}{{d1}^{\left(3 + 1\right)}} \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
  5. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{d1}^{9}} \cdot d1\]
  6. Using strategy rm
  7. Applied pow-plus0

    \[\leadsto \color{blue}{{d1}^{\left(9 + 1\right)}}\]
  8. Final simplification0

    \[\leadsto {d1}^{\left(9 + 1\right)}\]

Runtime

Time bar (total: 12.8s)Debug logProfile

herbie shell --seed 2018225 
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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