Average Error: 29.4 → 19.9
Time: 14.3s
Precision: 64
Internal Precision: 576
\[\frac{a \cdot a}{\left(a \cdot a\right) \cdot a - \left(b \cdot b\right) \cdot b}\]
\[\frac{a}{a - b} \cdot \frac{\frac{a}{\sqrt{b \cdot b + \left(b + a\right) \cdot a}}}{\sqrt{b \cdot b + \left(b + a\right) \cdot a}}\]

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

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Derivation

  1. Initial program 29.4

    \[\frac{a \cdot a}{\left(a \cdot a\right) \cdot a - \left(b \cdot b\right) \cdot b}\]
  2. Initial simplification29.4

    \[\leadsto \frac{a \cdot a}{{a}^{3} - {b}^{3}}\]
  3. Using strategy rm
  4. Applied difference-cubes30.0

    \[\leadsto \frac{a \cdot a}{\color{blue}{\left(a \cdot a + \left(b \cdot b + a \cdot b\right)\right) \cdot \left(a - b\right)}}\]
  5. Applied times-frac20.0

    \[\leadsto \color{blue}{\frac{a}{a \cdot a + \left(b \cdot b + a \cdot b\right)} \cdot \frac{a}{a - b}}\]
  6. Simplified19.9

    \[\leadsto \color{blue}{\frac{a}{b \cdot b + a \cdot \left(a + b\right)}} \cdot \frac{a}{a - b}\]
  7. Using strategy rm
  8. Applied add-sqr-sqrt19.9

    \[\leadsto \frac{a}{\color{blue}{\sqrt{b \cdot b + a \cdot \left(a + b\right)} \cdot \sqrt{b \cdot b + a \cdot \left(a + b\right)}}} \cdot \frac{a}{a - b}\]
  9. Applied associate-/r*19.9

    \[\leadsto \color{blue}{\frac{\frac{a}{\sqrt{b \cdot b + a \cdot \left(a + b\right)}}}{\sqrt{b \cdot b + a \cdot \left(a + b\right)}}} \cdot \frac{a}{a - b}\]
  10. Final simplification19.9

    \[\leadsto \frac{a}{a - b} \cdot \frac{\frac{a}{\sqrt{b \cdot b + \left(b + a\right) \cdot a}}}{\sqrt{b \cdot b + \left(b + a\right) \cdot a}}\]

Runtime

Time bar (total: 14.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (a b)
  :name "a*a / (a*a*a-b*b*b)"
  (/ (* a a) (- (* (* a a) a) (* (* b b) b))))