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

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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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))))