Average Error: 29.5 → 0.4
Time: 29.7s
Precision: 64
Internal Precision: 1344
$\sin \left(x + 1\right) - \sin x$
$\left(\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1} + \cos x \cdot \sin 1\right) - \sin x$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 29.5

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

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

$\leadsto \left(\sin x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} + \cos x \cdot \sin 1\right) - \sin x$
6. Applied associate-*r*0.4

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

# Runtime

Time bar (total: 29.7s)Debug log

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