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

# Try it out

Results

 In Out
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

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