Average Error: 0.0 → 0.0
Time: 10.0s
Precision: 64
Internal Precision: 320
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[(e^{\log_* (1 + x \cdot (x \cdot x + x)_*)} - 1)^*\]

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1.0 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]

  2. Initial simplification0.0

    \[\leadsto (\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*\]
  3. Using strategy rm

  4. Applied expm1-log1p-u0.0

    \[\leadsto \color{blue}{(e^{\log_* (1 + (\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*)} - 1)^*}\]
  5. Using strategy rm

  6. Applied expm1-log1p-u0.0

    \[\leadsto (e^{\log_* (1 + \color{blue}{(e^{\log_* (1 + (\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*)} - 1)^*})} - 1)^*\]

  7. Applied log1p-expm10.0

    \[\leadsto (e^{\color{blue}{\log_* (1 + (\left(x \cdot x\right) \cdot x + \left(x \cdot x\right))_*)}} - 1)^*\]

  8. Simplified0.0

    \[\leadsto (e^{\log_* (1 + \color{blue}{(x \cdot x + x)_* \cdot x})} - 1)^*\]

  9. Final simplification0.0

    \[\leadsto (e^{\log_* (1 + x \cdot (x \cdot x + x)_*)} - 1)^*\]

Runtime

Time bar (total: 10.0s)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))