Average Error: 29.8 → 0.2
Time: 37.3s
Precision: 64
Internal Precision: 2368
\[\frac{\left(\frac{\sin \left(\left(x + \varepsilon\right) - \varepsilon\right)}{\cos x \cdot \cos \varepsilon} \cdot \cos x\right) \cdot \cos \varepsilon}{\sin \varepsilon}\]
\[\frac{\sin x}{\sin \varepsilon}\]

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 29.8

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

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

Runtime

Time bar (total: 37.3s)Debug log

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