Average Error: 3.0 → 0.1
Time: 28.3s
Precision: 64
Internal Precision: 576
\[1 - a \cdot {\left(1 - b\right)}^{\left(\frac{3}{2}\right)}\]
\[1 - \left(a \cdot {\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}\right) \cdot {\left(1 - b\right)}^{\left(\frac{1}{2} \cdot \frac{3}{2}\right)}\]

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.0

    \[1 - a \cdot {\left(1 - b\right)}^{\left(\frac{3}{2}\right)}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt3.1

    \[\leadsto 1 - a \cdot {\color{blue}{\left(\sqrt{1 - b} \cdot \sqrt{1 - b}\right)}}^{\left(\frac{3}{2}\right)}\]
  4. Applied unpow-prod-down3.1

    \[\leadsto 1 - a \cdot \color{blue}{\left({\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}\right)}\]
  5. Applied associate-*r*0.2

    \[\leadsto 1 - \color{blue}{\left(a \cdot {\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}\right) \cdot {\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}\]
  6. Using strategy rm
  7. Applied pow1/20.2

    \[\leadsto 1 - \left(a \cdot {\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}\right) \cdot {\color{blue}{\left({\left(1 - b\right)}^{\frac{1}{2}}\right)}}^{\left(\frac{3}{2}\right)}\]
  8. Applied pow-pow0.1

    \[\leadsto 1 - \left(a \cdot {\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}\right) \cdot \color{blue}{{\left(1 - b\right)}^{\left(\frac{1}{2} \cdot \frac{3}{2}\right)}}\]

Runtime

Time bar (total: 28.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (a b)
  :name "(1 - a*(1 - b)^(3/2))"
  (- 1 (* a (pow (- 1 b) (/ 3 2)))))