Average Error: 48.6 → 8.3
Time: 33.3s
Precision: binary64
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↓
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Error

Bits error versus t

Bits error versus l

Bits error versus k

Derivation

  1. Initial program 48.6

    \[\]

  2. Simplified39.2

    \[\leadsto \]

  3. Taylor expanded around inf 52.3

    \[\leadsto \]

  4. Simplified15.8

    \[\leadsto \]
  5. Using strategy rm

  6. Applied sqr-pow15.8

    \[\leadsto \]

  7. Applied unpow-prod-down15.8

    \[\leadsto \]

  8. Applied associate-*l*12.7

    \[\leadsto \]

  9. Simplified12.7

    \[\leadsto \]
  10. Using strategy rm

  11. Applied unpow-prod-down12.7

    \[\leadsto \]

  12. Applied associate-*l*8.3

    \[\leadsto \]

  13. Simplified9.7

    \[\leadsto \]
  14. Using strategy rm

  15. Applied associate-*r*8.3

    \[\leadsto \]

  16. Final simplification8.3

    \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10-)"
  :precision binary64
  (/ 2.0 (* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (- (+ 1.0 (pow (/ k t) 2.0)) 1.0))))