Average Error: 61.0 → 31.7
Time: 5.6s
Precision: 64
Internal Precision: 2368
\[(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*\]
\[\log \left(\sqrt{e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}}\right) + \log \left(\sqrt{e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}}\right)\]

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 61.0

    \[(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*\]
  2. Using strategy rm
  3. Applied add-log-exp31.7

    \[\leadsto \color{blue}{\log \left(e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}\right)}\]
  4. Using strategy rm
  5. Applied add-sqr-sqrt31.7

    \[\leadsto \log \color{blue}{\left(\sqrt{e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}} \cdot \sqrt{e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}}\right)}\]
  6. Applied log-prod31.7

    \[\leadsto \color{blue}{\log \left(\sqrt{e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}}\right) + \log \left(\sqrt{e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}}\right)}\]
  7. Final simplification31.7

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

Runtime

Time bar (total: 5.6s)Debug log

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