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

# Try it out

Results

 In Out
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))))