Average Error: 14.0 → 0.3
Time: 2.2m
Precision: 64
Internal Precision: 320
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
↓
\[\frac{\frac{\frac{1}{a} - \frac{1}{b}}{\left(a + b\right) \cdot 2}}{\frac{b - a}{\pi}}\]

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 14.0

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

  2. Applied simplify0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{a} - \frac{1}{b}}{\left(a + b\right) \cdot 2} \cdot \frac{\pi}{b - a}}\]
  3. Using strategy rm

  4. Applied clear-num0.3

    \[\leadsto \frac{\frac{1}{a} - \frac{1}{b}}{\left(a + b\right) \cdot 2} \cdot \color{blue}{\frac{1}{\frac{b - a}{\pi}}}\]
  5. Using strategy rm

  6. Applied un-div-inv0.3

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

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed 2018296 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))