\[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
Test:
simple fma test
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Time: 9.3 s
Input Error: 19.8
Output Error: 16.2
Log: ⚲
Profile: 🕒
\(\frac{{\left((x * y + z)_*\right)}^3 - 1}{\frac{{\left({\left((x * y + z)_*\right)}^2\right)}^2 - {\left({1}^2 + (x * y + z)_* \cdot 1\right)}^2}{{\left((x * y + z)_*\right)}^2 - \left({1}^2 + (x * y + z)_* \cdot 1\right)}} - \left(x \cdot y + z\right)\)
  1. Started with
    \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
    19.8
  2. Using strategy rm
    19.8
  3. Applied associate--r+ to get
    \[\color{red}{(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \leadsto \color{blue}{\left((x * y + z)_* - 1\right) - \left(x \cdot y + z\right)}\]
    15.8
  4. Using strategy rm
    15.8
  5. Applied flip3-- to get
    \[\color{red}{\left((x * y + z)_* - 1\right)} - \left(x \cdot y + z\right) \leadsto \color{blue}{\frac{{\left((x * y + z)_*\right)}^{3} - {1}^{3}}{{\left((x * y + z)_*\right)}^2 + \left({1}^2 + (x * y + z)_* \cdot 1\right)}} - \left(x \cdot y + z\right)\]
    21.0
  6. Applied simplify to get
    \[\frac{\color{red}{{\left((x * y + z)_*\right)}^{3} - {1}^{3}}}{{\left((x * y + z)_*\right)}^2 + \left({1}^2 + (x * y + z)_* \cdot 1\right)} - \left(x \cdot y + z\right) \leadsto \frac{\color{blue}{{\left((x * y + z)_*\right)}^3 - 1}}{{\left((x * y + z)_*\right)}^2 + \left({1}^2 + (x * y + z)_* \cdot 1\right)} - \left(x \cdot y + z\right)\]
    16.2
  7. Using strategy rm
    16.2
  8. Applied flip-+ to get
    \[\frac{{\left((x * y + z)_*\right)}^3 - 1}{\color{red}{{\left((x * y + z)_*\right)}^2 + \left({1}^2 + (x * y + z)_* \cdot 1\right)}} - \left(x \cdot y + z\right) \leadsto \frac{{\left((x * y + z)_*\right)}^3 - 1}{\color{blue}{\frac{{\left({\left((x * y + z)_*\right)}^2\right)}^2 - {\left({1}^2 + (x * y + z)_* \cdot 1\right)}^2}{{\left((x * y + z)_*\right)}^2 - \left({1}^2 + (x * y + z)_* \cdot 1\right)}}} - \left(x \cdot y + z\right)\]
    16.2

Original test:


(lambda ((x default) (y default) (z default))
  #:name "simple fma test"
  (- (fma x y z) (+ 1 (+ (* x y) z)))
  #:target
  -1)