Average Error: 0.3 → 0.2
Time: 28.1s
Precision: 64
Internal Precision: 576
\[\frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}\]
\[\frac{1}{\cos x} \cdot \tan \varepsilon\]

Error

Bits error versus eps

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}\]
  2. Using strategy rm
  3. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\color{blue}{1 \cdot \sin \varepsilon}}{\cos x \cdot \cos \varepsilon}\]
  4. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{1}{\cos x} \cdot \frac{\sin \varepsilon}{\cos \varepsilon}}\]
  5. Using strategy rm
  6. Applied quot-tan0.2

    \[\leadsto \frac{1}{\cos x} \cdot \color{blue}{\tan \varepsilon}\]

Runtime

Time bar (total: 28.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (eps x)
  :name "sin(eps)/(cos(x)*cos(eps))"
  (/ (sin eps) (* (cos x) (cos eps))))