Average Error: 62.5 → 47.0
Time: 37.5s
Precision: 64
Internal Precision: 128
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
↓
\[0\]

Error

Bits error versus a

Bits error versus b

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Results

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Derivation

  1. Initial program 62.5

    \[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]

  2. Initial simplification62.5

    \[\leadsto \frac{\frac{1}{a} - \frac{1}{b}}{b - a} \cdot \frac{\frac{\pi}{2}}{a + b}\]

  3. Taylor expanded around 0 47.0

    \[\leadsto \color{blue}{0}\]

  4. Final simplification47.0

    \[\leadsto 0\]

Runtime

Time bar (total: 37.5s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))