Average Error: 12.9 → 12.9
Time: 18.2s
Precision: 64
Internal Precision: 576
${sin}^{2} \cdot x + {cos}^{2} \cdot x$
$\sqrt{cos \cdot cos + sin \cdot sin} \cdot \left(x \cdot \sqrt{cos \cdot cos + sin \cdot sin}\right)$

# Try it out

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# Derivation

1. Initial program 12.9

${sin}^{2} \cdot x + {cos}^{2} \cdot x$
2. Initial simplification12.9

$\leadsto x \cdot \left(cos \cdot cos + sin \cdot sin\right)$
3. Using strategy rm

$\leadsto x \cdot \color{blue}{\left(\sqrt{cos \cdot cos + sin \cdot sin} \cdot \sqrt{cos \cdot cos + sin \cdot sin}\right)}$
5. Applied associate-*r*12.9

$\leadsto \color{blue}{\left(x \cdot \sqrt{cos \cdot cos + sin \cdot sin}\right) \cdot \sqrt{cos \cdot cos + sin \cdot sin}}$
6. Final simplification12.9

$\leadsto \sqrt{cos \cdot cos + sin \cdot sin} \cdot \left(x \cdot \sqrt{cos \cdot cos + sin \cdot sin}\right)$

# Runtime

Time bar (total: 18.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (sin x cos)
:name "sin^2 x + cos^2 x"
(+ (* (pow sin 2) x) (* (pow cos 2) x)))