Average Error: 29.5 → 0.6
Time: 29.6s
Precision: 64
Internal Precision: 1344
\[\frac{1}{\sin x} - \frac{1}{\sin \left(x - 1\right)}\]
\[\frac{1}{\sin x} - \frac{1}{\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1} + \cos x \cdot \sin \left(-1\right)}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.5

    \[\frac{1}{\sin x} - \frac{1}{\sin \left(x - 1\right)}\]
  2. Using strategy rm
  3. Applied sub-neg29.5

    \[\leadsto \frac{1}{\sin x} - \frac{1}{\sin \color{blue}{\left(x + \left(-1\right)\right)}}\]
  4. Applied sin-sum0.6

    \[\leadsto \frac{1}{\sin x} - \frac{1}{\color{blue}{\sin x \cdot \cos \left(-1\right) + \cos x \cdot \sin \left(-1\right)}}\]
  5. Applied simplify0.6

    \[\leadsto \frac{1}{\sin x} - \frac{1}{\color{blue}{\sin x \cdot \cos 1} + \cos x \cdot \sin \left(-1\right)}\]
  6. Using strategy rm
  7. Applied add-cube-cbrt0.7

    \[\leadsto \frac{1}{\sin x} - \frac{1}{\sin x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} + \cos x \cdot \sin \left(-1\right)}\]
  8. Applied associate-*r*0.6

    \[\leadsto \frac{1}{\sin x} - \frac{1}{\color{blue}{\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1}} + \cos x \cdot \sin \left(-1\right)}\]

Runtime

Time bar (total: 29.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "1/sin(x)-1/(sin(x-1))"
  (- (/ 1 (sin x)) (/ 1 (sin (- x 1)))))