Average Error: 61.1 → 61.1
Time: 27.6s
Precision: 64
Internal Precision: 2368
\[\frac{\sin^{-1} x - x}{{x}^{3}}\]
\[\frac{\frac{{\left(\sin^{-1} x\right)}^{3} \cdot {\left(\sin^{-1} x\right)}^{3} - {x}^{3} \cdot {x}^{3}}{{x}^{3} + {\left(\sin^{-1} x\right)}^{3}}}{{x}^{3} \cdot \left(\sin^{-1} x \cdot \sin^{-1} x + \left(x \cdot \sin^{-1} x + x \cdot x\right)\right)}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.1

    \[\frac{\sin^{-1} x - x}{{x}^{3}}\]
  2. Using strategy rm
  3. Applied flip3--61.1

    \[\leadsto \frac{\color{blue}{\frac{{\left(\sin^{-1} x\right)}^{3} - {x}^{3}}{\sin^{-1} x \cdot \sin^{-1} x + \left(x \cdot x + \sin^{-1} x \cdot x\right)}}}{{x}^{3}}\]
  4. Applied associate-/l/61.1

    \[\leadsto \color{blue}{\frac{{\left(\sin^{-1} x\right)}^{3} - {x}^{3}}{{x}^{3} \cdot \left(\sin^{-1} x \cdot \sin^{-1} x + \left(x \cdot x + \sin^{-1} x \cdot x\right)\right)}}\]
  5. Using strategy rm
  6. Applied flip--61.1

    \[\leadsto \frac{\color{blue}{\frac{{\left(\sin^{-1} x\right)}^{3} \cdot {\left(\sin^{-1} x\right)}^{3} - {x}^{3} \cdot {x}^{3}}{{\left(\sin^{-1} x\right)}^{3} + {x}^{3}}}}{{x}^{3} \cdot \left(\sin^{-1} x \cdot \sin^{-1} x + \left(x \cdot x + \sin^{-1} x \cdot x\right)\right)}\]
  7. Final simplification61.1

    \[\leadsto \frac{\frac{{\left(\sin^{-1} x\right)}^{3} \cdot {\left(\sin^{-1} x\right)}^{3} - {x}^{3} \cdot {x}^{3}}{{x}^{3} + {\left(\sin^{-1} x\right)}^{3}}}{{x}^{3} \cdot \left(\sin^{-1} x \cdot \sin^{-1} x + \left(x \cdot \sin^{-1} x + x \cdot x\right)\right)}\]

Runtime

Time bar (total: 27.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "(asin(x)-x)/x^3"
  (/ (- (asin x) x) (pow x 3)))