Average Error: 30.2 → 0.3
Time: 34.7s
Precision: 64
Internal Precision: 2368
\[\frac{\sin \left(\left(x + \varepsilon\right) - x\right)}{\cos x \cdot \cos \varepsilon}\]
\[\frac{\sin \varepsilon}{\cos x} \cdot \frac{1}{\cos \varepsilon}\]

Error

Bits error versus x

Bits error versus eps

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.2

    \[\frac{\sin \left(\left(x + \varepsilon\right) - x\right)}{\cos x \cdot \cos \varepsilon}\]
  2. Applied simplify0.3

    \[\leadsto \color{blue}{\frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}}\]
  3. Using strategy rm
  4. Applied associate-/r*0.3

    \[\leadsto \color{blue}{\frac{\frac{\sin \varepsilon}{\cos x}}{\cos \varepsilon}}\]
  5. Using strategy rm
  6. Applied div-inv0.3

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

Runtime

Time bar (total: 34.7s)Debug log

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