Average Error: 58.1 → 58.1
Time: 45.0s
Precision: 64
Internal Precision: 384
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\left((e^{\log_* (1 + 1314174534371215466459037696 \cdot 333.75)} - 1)^* + \frac{(\left(2982717960244805440196959278257715859509800802206226837608419884111561210238575275846436156793848210502189056 \cdot 5.5\right) \cdot \left(5.5 \cdot 5.5\right) + -496249783112017350686414974728164423066542512886734178162545340683796439796458124993939025060021149513414869000)_*}{(\left(2072087668778481942361612104703059945972513386907210959776023202964176896 \cdot 5.5\right) \cdot 5.5 + 62680658925530399348651842681623303061242097389084458210685414452745732100)_* + 5.5 \cdot 11396482809643571430007812120052271188174761835364336603425588735157207040}\right) + \frac{77617}{2 \cdot 33096}\]

Error

Derivation

  1. Initial program 58.1

    \[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
  2. Using strategy rm

  3. Applied associate-+l+58.1

    \[\leadsto \color{blue}{\left(333.75 \cdot {33096}^{6} + \left(\left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right) + 5.5 \cdot {33096}^{8}\right)\right)} + \frac{77617}{2 \cdot 33096}\]

  4. Applied simplify58.1

    \[\leadsto \left(333.75 \cdot {33096}^{6} + \color{blue}{(1439474789212538429291115400277262336 \cdot 5.5 + \left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right))_*}\right) + \frac{77617}{2 \cdot 33096}\]
  5. Using strategy rm

  6. Applied fma-udef58.1

    \[\leadsto \left(333.75 \cdot {33096}^{6} + \color{blue}{\left(1439474789212538429291115400277262336 \cdot 5.5 + \left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right)\right)}\right) + \frac{77617}{2 \cdot 33096}\]
  7. Using strategy rm

  8. Applied flip3-+58.1

    \[\leadsto \left(333.75 \cdot {33096}^{6} + \color{blue}{\frac{{\left(1439474789212538429291115400277262336 \cdot 5.5\right)}^{3} + {\left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right)}^{3}}{\left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right) + \left(\left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right) \cdot \left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right)\right)}}\right) + \frac{77617}{2 \cdot 33096}\]

  9. Applied simplify58.1

    \[\leadsto \left(333.75 \cdot {33096}^{6} + \frac{\color{blue}{(\left(2982717960244805440196959278257715859509800802206226837608419884111561210238575275846436156793848210502189056 \cdot 5.5\right) \cdot \left(5.5 \cdot 5.5\right) + -496249783112017350686414974728164423066542512886734178162545340683796439796458124993939025060021149513414869000)_*}}{\left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right) + \left(\left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right) \cdot \left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(-874583152769217411136394072064 + -7917110904691559438276885495834701826\right)\right)}\right) + \frac{77617}{2 \cdot 33096}\]

  10. Applied simplify58.1

    \[\leadsto \left(333.75 \cdot {33096}^{6} + \frac{(\left(2982717960244805440196959278257715859509800802206226837608419884111561210238575275846436156793848210502189056 \cdot 5.5\right) \cdot \left(5.5 \cdot 5.5\right) + -496249783112017350686414974728164423066542512886734178162545340683796439796458124993939025060021149513414869000)_*}{\color{blue}{(\left(2072087668778481942361612104703059945972513386907210959776023202964176896 \cdot 5.5\right) \cdot 5.5 + 62680658925530399348651842681623303061242097389084458210685414452745732100)_* + 5.5 \cdot 11396482809643571430007812120052271188174761835364336603425588735157207040}}\right) + \frac{77617}{2 \cdot 33096}\]
  11. Using strategy rm

  12. Applied expm1-log1p-u58.1

    \[\leadsto \left(\color{blue}{(e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^*} + \frac{(\left(2982717960244805440196959278257715859509800802206226837608419884111561210238575275846436156793848210502189056 \cdot 5.5\right) \cdot \left(5.5 \cdot 5.5\right) + -496249783112017350686414974728164423066542512886734178162545340683796439796458124993939025060021149513414869000)_*}{(\left(2072087668778481942361612104703059945972513386907210959776023202964176896 \cdot 5.5\right) \cdot 5.5 + 62680658925530399348651842681623303061242097389084458210685414452745732100)_* + 5.5 \cdot 11396482809643571430007812120052271188174761835364336603425588735157207040}\right) + \frac{77617}{2 \cdot 33096}\]

  13. Applied simplify58.1

    \[\leadsto \left((e^{\color{blue}{\log_* (1 + 1314174534371215466459037696 \cdot 333.75)}} - 1)^* + \frac{(\left(2982717960244805440196959278257715859509800802206226837608419884111561210238575275846436156793848210502189056 \cdot 5.5\right) \cdot \left(5.5 \cdot 5.5\right) + -496249783112017350686414974728164423066542512886734178162545340683796439796458124993939025060021149513414869000)_*}{(\left(2072087668778481942361612104703059945972513386907210959776023202964176896 \cdot 5.5\right) \cdot 5.5 + 62680658925530399348651842681623303061242097389084458210685414452745732100)_* + 5.5 \cdot 11396482809643571430007812120052271188174761835364336603425588735157207040}\right) + \frac{77617}{2 \cdot 33096}\]

Runtime

Time bar (total: 45.0s)Debug logProfile

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' +o rules:numerics
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  (+ (+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096))))