Average Error: 61.0 → 31.0
Time: 5.4s
Precision: 64
Internal Precision: 2368
\[(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*\]
\[\log \left(\sqrt[3]{\left(e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*} \cdot e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*}\right) \cdot e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*}}\right)\]

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 61.0

    \[(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*\]
  2. Using strategy rm
  3. Applied add-log-exp31.0

    \[\leadsto \color{blue}{\log \left(e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*}\right)}\]
  4. Using strategy rm
  5. Applied add-cbrt-cube31.0

    \[\leadsto \log \color{blue}{\left(\sqrt[3]{\left(e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*} \cdot e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*}\right) \cdot e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*}}\right)}\]
  6. Final simplification31.0

    \[\leadsto \log \left(\sqrt[3]{\left(e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*} \cdot e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*}\right) \cdot e^{(\left(x \cdot y\right) \cdot \left(\frac{1}{x}\right) + \left(-y\right))_*}}\right)\]

Runtime

Time bar (total: 5.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x y)
  :name "fma(x*y,1/x,-y)"
  (fma (* x y) (/ 1 x) (- y)))