Average Error: 2.4 → 0.1
Time: 43.2s
Precision: 64
Internal Precision: 576
\[{\left(\left(1 + {g}^{2}\right) - 2 \cdot \left(g \cdot x\right)\right)}^{\left(-1.5\right)}\]
\[{\left(1 + g \cdot \left(g - x \cdot 2\right)\right)}^{\left(-1.5\right)}\]

Error

Bits error versus g

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.4

    \[{\left(\left(1 + {g}^{2}\right) - 2 \cdot \left(g \cdot x\right)\right)}^{\left(-1.5\right)}\]
  2. Using strategy rm
  3. Applied associate--l+2.4

    \[\leadsto {\color{blue}{\left(1 + \left({g}^{2} - 2 \cdot \left(g \cdot x\right)\right)\right)}}^{\left(-1.5\right)}\]
  4. Applied simplify0.1

    \[\leadsto {\left(1 + \color{blue}{g \cdot \left(g - x \cdot 2\right)}\right)}^{\left(-1.5\right)}\]

Runtime

Time bar (total: 43.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (g x)
  :name "(1 + g^2 - 2g*x)^(-1.5)"
  (pow (- (+ 1 (pow g 2)) (* 2 (* g x))) (- 1.5)))