Average Error: 62.5 → 47.0
Time: 1.2m
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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  3. Taylor expanded around inf 47.0

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

  4. Final simplification47.0

    \[\leadsto 0\]

Runtime

Time bar (total: 1.2m)Debug logProfile

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