Average Error: 14.8 → 0.4
Time: 11.7s
Precision: 64
Internal Precision: 1344
$\sin \left(y - x\right) - \cos \left(x - y\right)$
$\cos x \cdot \sin y - \left(\left(\sin x \cdot \sin y + \cos y \cdot \cos x\right) + \sin x \cdot \cos y\right)$

# Try it out

Results

 In Out
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# Derivation

1. Initial program 14.8

$\sin \left(y - x\right) - \cos \left(x - y\right)$
2. Initial simplification14.8

$\leadsto \sin \left(y - x\right) - \cos \left(x - y\right)$
3. Using strategy rm
4. Applied cos-diff14.3

$\leadsto \sin \left(y - x\right) - \color{blue}{\left(\cos x \cdot \cos y + \sin x \cdot \sin y\right)}$
5. Using strategy rm
6. Applied sin-diff0.4

$\leadsto \color{blue}{\left(\sin y \cdot \cos x - \cos y \cdot \sin x\right)} - \left(\cos x \cdot \cos y + \sin x \cdot \sin y\right)$
7. Applied associate--l-0.4

$\leadsto \color{blue}{\sin y \cdot \cos x - \left(\cos y \cdot \sin x + \left(\cos x \cdot \cos y + \sin x \cdot \sin y\right)\right)}$
8. Final simplification0.4

$\leadsto \cos x \cdot \sin y - \left(\left(\sin x \cdot \sin y + \cos y \cdot \cos x\right) + \sin x \cdot \cos y\right)$

# Runtime

Time bar (total: 11.7s)Debug log

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