Average Error: 7.8 → 7.9
Time: 37.3s
Precision: 64
Internal Precision: 2112
\[\cos^{-1} \left(\sin x \cdot \sin y + \left(\cos x \cdot \cos y\right) \cdot \cos z\right)\]
\[\log \left({e}^{\left(\cos^{-1} \left(\sin y \cdot \sin x + \cos z \cdot \left(\cos x \cdot \cos y\right)\right)\right)}\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 7.8

    \[\cos^{-1} \left(\sin x \cdot \sin y + \left(\cos x \cdot \cos y\right) \cdot \cos z\right)\]
  2. Using strategy rm
  3. Applied add-log-exp7.8

    \[\leadsto \color{blue}{\log \left(e^{\cos^{-1} \left(\sin x \cdot \sin y + \left(\cos x \cdot \cos y\right) \cdot \cos z\right)}\right)}\]
  4. Using strategy rm
  5. Applied *-un-lft-identity7.8

    \[\leadsto \log \left(e^{\color{blue}{1 \cdot \cos^{-1} \left(\sin x \cdot \sin y + \left(\cos x \cdot \cos y\right) \cdot \cos z\right)}}\right)\]
  6. Applied exp-prod7.9

    \[\leadsto \log \color{blue}{\left({\left(e^{1}\right)}^{\left(\cos^{-1} \left(\sin x \cdot \sin y + \left(\cos x \cdot \cos y\right) \cdot \cos z\right)\right)}\right)}\]
  7. Simplified7.9

    \[\leadsto \log \left({\color{blue}{e}}^{\left(\cos^{-1} \left(\sin x \cdot \sin y + \left(\cos x \cdot \cos y\right) \cdot \cos z\right)\right)}\right)\]
  8. Final simplification7.9

    \[\leadsto \log \left({e}^{\left(\cos^{-1} \left(\sin y \cdot \sin x + \cos z \cdot \left(\cos x \cdot \cos y\right)\right)\right)}\right)\]

Runtime

Time bar (total: 37.3s)Debug log

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