Average Error: 0.1 → 0.1
Time: 12.8s
Precision: 64
Internal Precision: 576
\[\sqrt{x} \cdot \sin 45 - \cos 33\]
\[\sqrt{\left(\sin 45 \cdot x\right) \cdot \sin 45} - \cos 33\]

Error

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Results

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Derivation

  1. Initial program 0.1

    \[\sqrt{x} \cdot \sin 45 - \cos 33\]
  2. Initial simplification0.1

    \[\leadsto \sin 45 \cdot \sqrt{x} - \cos 33\]
  3. Using strategy rm
  4. Applied add-sqr-sqrt0.1

    \[\leadsto \color{blue}{\left(\sqrt{\sin 45} \cdot \sqrt{\sin 45}\right)} \cdot \sqrt{x} - \cos 33\]
  5. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\sqrt{\sin 45} \cdot \left(\sqrt{\sin 45} \cdot \sqrt{x}\right)} - \cos 33\]
  6. Using strategy rm
  7. Applied sqrt-unprod0.1

    \[\leadsto \sqrt{\sin 45} \cdot \color{blue}{\sqrt{\sin 45 \cdot x}} - \cos 33\]
  8. Applied sqrt-unprod0.1

    \[\leadsto \color{blue}{\sqrt{\sin 45 \cdot \left(\sin 45 \cdot x\right)}} - \cos 33\]
  9. Final simplification0.1

    \[\leadsto \sqrt{\left(\sin 45 \cdot x\right) \cdot \sin 45} - \cos 33\]

Runtime

Time bar (total: 12.8s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "sqrt(x)*sin(45)-cos(33)"
  (- (* (sqrt x) (sin 45)) (cos 33)))