Average Error: 30.8 → 29.6
Time: 20.0s
Precision: 64
Internal Precision: 2368
$\sin \left(x \cdot x\right) - \sin \left(x \cdot x + 1\right)$
$\sin \left(x \cdot x\right) - \left(\cos \left(x \cdot x\right) \cdot \sin 1 + \sqrt[3]{\cos 1 \cdot \sin \left(x \cdot x\right)} \cdot \left(\sqrt[3]{\cos 1 \cdot \sin \left(x \cdot x\right)} \cdot \sqrt[3]{\cos 1 \cdot \sin \left(x \cdot x\right)}\right)\right)$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 30.8

$\sin \left(x \cdot x\right) - \sin \left(x \cdot x + 1\right)$
2. Initial simplification30.8

$\leadsto \sin \left(x \cdot x\right) - \sin \left(x \cdot x + 1\right)$
3. Using strategy rm
4. Applied sin-sum29.6

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

$\leadsto \sin \left(x \cdot x\right) - \left(\color{blue}{\left(\sqrt[3]{\sin \left(x \cdot x\right) \cdot \cos 1} \cdot \sqrt[3]{\sin \left(x \cdot x\right) \cdot \cos 1}\right) \cdot \sqrt[3]{\sin \left(x \cdot x\right) \cdot \cos 1}} + \cos \left(x \cdot x\right) \cdot \sin 1\right)$
7. Final simplification29.6

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

# Runtime

Time bar (total: 20.0s)Debug log

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