Average Error: 15.3 → 0.2
Time: 12.3s
Precision: 64
Internal Precision: 1344
$\cos x - 1$
$0 - \sin x \cdot \tan \left(\frac{x}{2}\right)$

# Try it out

Results

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# Derivation

1. Initial program 15.3

$\cos x - 1$
2. Using strategy rm
3. Applied flip--15.6

$\leadsto \color{blue}{\frac{\cos x \cdot \cos x - 1 \cdot 1}{\cos x + 1}}$
4. Applied simplify0.6

$\leadsto \frac{\color{blue}{-\sin x \cdot \sin x}}{\cos x + 1}$
5. Using strategy rm
6. Applied neg-sub00.6

$\leadsto \frac{\color{blue}{0 - \sin x \cdot \sin x}}{\cos x + 1}$
7. Applied div-sub0.6

$\leadsto \color{blue}{\frac{0}{\cos x + 1} - \frac{\sin x \cdot \sin x}{\cos x + 1}}$
8. Applied simplify0.6

$\leadsto \color{blue}{0} - \frac{\sin x \cdot \sin x}{\cos x + 1}$
9. Applied simplify0.2

$\leadsto 0 - \color{blue}{\sin x \cdot \tan \left(\frac{x}{2}\right)}$

# Runtime

Time bar (total: 12.3s)Debug log

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