Average Error: 29.3 → 29.4
Time: 9.0s
Precision: 64
Internal Precision: 576
$\log \left(\left|\sin x\right| + 1\right) + \cos \left(x \cdot x\right)$
$\frac{\cos \left(x \cdot x\right) \cdot \left(\sqrt[3]{\cos \left(x \cdot x\right)} \cdot \left(\sqrt[3]{\cos \left(x \cdot x\right)} \cdot \sqrt[3]{\cos \left(x \cdot x\right)}\right)\right) - \log \left(1 + \left|\sin x\right|\right) \cdot \log \left(1 + \left|\sin x\right|\right)}{\cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right)}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 29.3

$\log \left(\left|\sin x\right| + 1\right) + \cos \left(x \cdot x\right)$
2. Initial simplification29.3

$\leadsto \cos \left(x \cdot x\right) + \log \left(1 + \left|\sin x\right|\right)$
3. Using strategy rm
4. Applied flip-+29.3

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

$\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{\cos \left(x \cdot x\right)} \cdot \sqrt[3]{\cos \left(x \cdot x\right)}\right) \cdot \sqrt[3]{\cos \left(x \cdot x\right)}\right)} \cdot \cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right) \cdot \log \left(1 + \left|\sin x\right|\right)}{\cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right)}$
7. Final simplification29.4

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

# Runtime

Time bar (total: 9.0s)Debug log

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