Average Error: 29.5 → 0.3
Time: 15.3s
Precision: 64
Internal Precision: 1344
$\sin \left(x + 1\right) - \sin x$
$\cos x \cdot \sin 1 + \left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \left(\sin x \cdot \sqrt[3]{\cos 1}\right) - \sin x\right)$

# Try it out

Results

 In Out
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# Derivation

1. Initial program 29.5

$\sin \left(x + 1\right) - \sin x$
2. Initial simplification29.5

$\leadsto \sin \left(1 + x\right) - \sin x$
3. Using strategy rm
4. Applied sin-sum0.4

$\leadsto \color{blue}{\left(\sin 1 \cdot \cos x + \cos 1 \cdot \sin x\right)} - \sin x$
5. Applied associate--l+0.4

$\leadsto \color{blue}{\sin 1 \cdot \cos x + \left(\cos 1 \cdot \sin x - \sin x\right)}$
6. Using strategy rm

$\leadsto \sin 1 \cdot \cos x + \left(\color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} \cdot \sin x - \sin x\right)$
8. Applied associate-*l*0.3

$\leadsto \sin 1 \cdot \cos x + \left(\color{blue}{\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \left(\sqrt[3]{\cos 1} \cdot \sin x\right)} - \sin x\right)$
9. Final simplification0.3

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

# Runtime

Time bar (total: 15.3s)Debug log

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