Average Error: 45.2 → 0
Time: 3.2s
Precision: 64
Internal Precision: 2432
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[\log \left(\frac{1}{e}\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.2
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.2

    \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]

  2. Applied simplify29.4

    \[\leadsto \color{blue}{\left(z - 1\right) - z}\]
  3. Using strategy rm

  4. Applied add-log-exp29.4

    \[\leadsto \color{blue}{\log \left(e^{\left(z - 1\right) - z}\right)}\]

  5. Applied simplify0

    \[\leadsto \log \color{blue}{\left(\frac{1}{e}\right)}\]

Runtime

Time bar (total: 3.2s)Debug logProfile

herbie shell --seed '#(1064269945 2896236262 301053905 1701069080 1701464310 1614783279)' +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

  (- (fma x y z) (+ 1 (+ (* x y) z))))