\[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
Test:
simple fma test
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Time: 12.9 s
Input Error: 45.3
Output Error: 15.1
Log: ⚲
Profile: 🕒
\(\log \left(e^{\left(\left((x * y + z)_* - z\right) - y \cdot x\right) - 1}\right)\)
  1. Started with
    \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
    45.3
  2. Using strategy rm
    45.3
  3. Applied add-cbrt-cube to get
    \[(x * y + z)_* - \left(1 + \color{red}{\left(x \cdot y + z\right)}\right) \leadsto (x * y + z)_* - \left(1 + \color{blue}{\sqrt[3]{{\left(x \cdot y + z\right)}^3}}\right)\]
    45.9
  4. Using strategy rm
    45.9
  5. Applied add-log-exp to get
    \[\color{red}{(x * y + z)_* - \left(1 + \sqrt[3]{{\left(x \cdot y + z\right)}^3}\right)} \leadsto \color{blue}{\log \left(e^{(x * y + z)_* - \left(1 + \sqrt[3]{{\left(x \cdot y + z\right)}^3}\right)}\right)}\]
    46.0
  6. Applied simplify to get
    \[\log \color{red}{\left(e^{(x * y + z)_* - \left(1 + \sqrt[3]{{\left(x \cdot y + z\right)}^3}\right)}\right)} \leadsto \log \color{blue}{\left(e^{\left((x * y + z)_* - z\right) - \left(y \cdot x + 1\right)}\right)}\]
    30.8
  7. Using strategy rm
    30.8
  8. Applied associate--r+ to get
    \[\log \left(e^{\color{red}{\left((x * y + z)_* - z\right) - \left(y \cdot x + 1\right)}}\right) \leadsto \log \left(e^{\color{blue}{\left(\left((x * y + z)_* - z\right) - y \cdot x\right) - 1}}\right)\]
    15.1

Original test:


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