Average Error: 0.3 → 0.3
Time: 17.1s
Precision: 64
Internal Precision: 576
\[\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y \cdot \sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]
\[\frac{\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y}}{\sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y \cdot \sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]
  2. Initial simplification0.3

    \[\leadsto \frac{\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y}}{\sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]
  3. Final simplification0.3

    \[\leadsto \frac{\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y}}{\sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]

Runtime

Time bar (total: 17.1s)Debug log

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