Average Error: 0.3 → 0.2
Time: 14.4s
Precision: 64
Internal Precision: 576
$\left(\sin x - \cos y\right) + \mathsf{erf} \left(\sqrt{x}\right)$
$\frac{\sin x \cdot \sin x - \left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right) \cdot \left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right)}{\left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right) + \sin x}$

# Try it out

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# Derivation

1. Initial program 0.3

$\left(\sin x - \cos y\right) + \mathsf{erf} \left(\sqrt{x}\right)$
2. Using strategy rm
3. Applied associate-+l-0.1

$\leadsto \color{blue}{\sin x - \left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right)}$
4. Using strategy rm
5. Applied flip--0.2

$\leadsto \color{blue}{\frac{\sin x \cdot \sin x - \left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right) \cdot \left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right)}{\sin x + \left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right)}}$
6. Final simplification0.2

$\leadsto \frac{\sin x \cdot \sin x - \left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right) \cdot \left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right)}{\left(\cos y - \mathsf{erf} \left(\sqrt{x}\right)\right) + \sin x}$

# Runtime

Time bar (total: 14.4s)Debug log

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