Average Error: 45.2 → 13.2
Time: 24.0s
Precision: 64
Internal Precision: 2368
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[\left(\left((x \cdot y + z)_* - x \cdot y\right) - z\right) - 1\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.2
Target0
Herbie13.2
\[-1\]

Derivation

  1. Initial program 45.2

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

  2. Initial simplification34.2

    \[\leadsto \left((x \cdot y + z)_* - x \cdot y\right) - \left(z - -1\right)\]
  3. Using strategy rm

  4. Applied sub-neg34.2

    \[\leadsto \left((x \cdot y + z)_* - x \cdot y\right) - \color{blue}{\left(z + \left(--1\right)\right)}\]

  5. Applied associate--r+13.2

    \[\leadsto \color{blue}{\left(\left((x \cdot y + z)_* - x \cdot y\right) - z\right) - \left(--1\right)}\]

  6. Simplified13.2

    \[\leadsto \left(\left((x \cdot y + z)_* - x \cdot y\right) - z\right) - \color{blue}{1}\]

  7. Final simplification13.2

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

Runtime

Time bar (total: 24.0s)Debug logProfile

herbie shell --seed 2018258 
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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