Average Error: 61.0 → 31.7
Time: 4.6s
Precision: 64
Internal Precision: 2368
\[(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*\]
\[\log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right) + \log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}} \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right)\]

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 61.0

    \[(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*\]
  2. Initial simplification61.0

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

    \[\leadsto \color{blue}{\log \left(e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}\right)}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt31.7

    \[\leadsto \log \color{blue}{\left(\left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}} \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right) \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right)}\]
  7. Applied log-prod31.7

    \[\leadsto \color{blue}{\log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}} \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right) + \log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right)}\]
  8. Final simplification31.7

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

Runtime

Time bar (total: 4.6s)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))