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

# Try it out

Results

 In Out
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# 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

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