\[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
Test:
simple fma test
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Time: 7.6 s
Input Error: 45.1
Output Error: 15.1
Log: ⚲
Profile: 🕒
\({\left(\sqrt[3]{\left(\left((x * y + z)_* - z\right) - y \cdot x\right) - 1}\right)}^3\)
  1. Started with
    \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
    45.1
  2. Using strategy rm
    45.1
  3. Applied add-cube-cbrt to get
    \[(x * y + z)_* - \color{red}{\left(1 + \left(x \cdot y + z\right)\right)} \leadsto (x * y + z)_* - \color{blue}{{\left(\sqrt[3]{1 + \left(x \cdot y + z\right)}\right)}^3}\]
    45.7
  4. Using strategy rm
    45.7
  5. Applied add-cube-cbrt to get
    \[\color{red}{(x * y + z)_* - {\left(\sqrt[3]{1 + \left(x \cdot y + z\right)}\right)}^3} \leadsto \color{blue}{{\left(\sqrt[3]{(x * y + z)_* - {\left(\sqrt[3]{1 + \left(x \cdot y + z\right)}\right)}^3}\right)}^3}\]
    45.7
  6. Applied simplify to get
    \[{\color{red}{\left(\sqrt[3]{(x * y + z)_* - {\left(\sqrt[3]{1 + \left(x \cdot y + z\right)}\right)}^3}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\left((x * y + z)_* - z\right) - \left(y \cdot x + 1\right)}\right)}}^3\]
    30.7
  7. Using strategy rm
    30.7
  8. Applied associate--r+ to get
    \[{\left(\sqrt[3]{\color{red}{\left((x * y + z)_* - z\right) - \left(y \cdot x + 1\right)}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\left(\left((x * y + z)_* - z\right) - y \cdot x\right) - 1}}\right)}^3\]
    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)