Average Error: 15.8 → 1.5
Time: 9.4s
Precision: binary64
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↓
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Error

Bits error versus K

Bits error versus m

Bits error versus n

Bits error versus M

Bits error versus l

Derivation

  1. Initial program 15.8

    \[\]

  2. Simplified15.8

    \[\leadsto \]

  3. Taylor expanded around 0 1.5

    \[\leadsto \]
  4. Using strategy rm

  5. Applied add-log-exp13.7

    \[\leadsto \]

  6. Applied add-log-exp13.7

    \[\leadsto \]

  7. Applied sum-log13.7

    \[\leadsto \]

  8. Simplified1.5

    \[\leadsto \]
  9. Using strategy rm

  10. Applied add-cube-cbrt1.5

    \[\leadsto \]

  11. Applied log-prod1.5

    \[\leadsto \]

  12. Simplified1.5

    \[\leadsto \]
  13. Using strategy rm

  14. Applied add-sqr-sqrt1.5

    \[\leadsto \]

  15. Applied log-prod1.5

    \[\leadsto \]

  16. Final simplification1.5

    \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))