Average Error: 0.2 → 0.3
Time: 6.2s
Precision: 64
Internal Precision: 576
$\sin x - \cos x$
$\sin x - \log \left(e^{\cos x}\right)$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.2

$\sin x - \cos x$
2. Using strategy rm

$\leadsto \sin x - \color{blue}{\log \left(e^{\cos x}\right)}$

$\leadsto \color{blue}{\log \left(e^{\sin x}\right)} - \log \left(e^{\cos x}\right)$
5. Applied diff-log0.4

$\leadsto \color{blue}{\log \left(\frac{e^{\sin x}}{e^{\cos x}}\right)}$
6. Simplified0.3

$\leadsto \log \color{blue}{\left(e^{\sin x - \cos x}\right)}$
7. Using strategy rm
8. Applied exp-diff0.4

$\leadsto \log \color{blue}{\left(\frac{e^{\sin x}}{e^{\cos x}}\right)}$
9. Applied log-div0.4

$\leadsto \color{blue}{\log \left(e^{\sin x}\right) - \log \left(e^{\cos x}\right)}$
10. Simplified0.3

$\leadsto \color{blue}{\sin x} - \log \left(e^{\cos x}\right)$
11. Final simplification0.3

$\leadsto \sin x - \log \left(e^{\cos x}\right)$

# Runtime

Time bar (total: 6.2s)Debug log

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