Average Error: 3.0 → 1.6
Time: 42.4s
Precision: 64
Internal Precision: 576
$1 - \frac{a}{b} \cdot {\left(1 - \frac{c}{d}\right)}^{\left(\frac{3}{2}\right)}$
$1 - \left(a \cdot \frac{{\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}}{b}\right) \cdot {\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 3.0

$1 - \frac{a}{b} \cdot {\left(1 - \frac{c}{d}\right)}^{\left(\frac{3}{2}\right)}$
2. Using strategy rm

$\leadsto 1 - \frac{a}{b} \cdot {\color{blue}{\left(\sqrt{1 - \frac{c}{d}} \cdot \sqrt{1 - \frac{c}{d}}\right)}}^{\left(\frac{3}{2}\right)}$
4. Applied unpow-prod-down3.0

$\leadsto 1 - \frac{a}{b} \cdot \color{blue}{\left({\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}\right)}$
5. Applied associate-*r*1.4

$\leadsto 1 - \color{blue}{\left(\frac{a}{b} \cdot {\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}\right) \cdot {\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}}$
6. Using strategy rm
7. Applied div-inv1.4

$\leadsto 1 - \left(\color{blue}{\left(a \cdot \frac{1}{b}\right)} \cdot {\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}\right) \cdot {\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}$
8. Applied associate-*l*1.6

$\leadsto 1 - \color{blue}{\left(a \cdot \left(\frac{1}{b} \cdot {\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}\right)\right)} \cdot {\left(\sqrt{1 - \frac{c}{d}}\right)}^{\left(\frac{3}{2}\right)}$
9. Applied simplify1.6

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

# Runtime

Time bar (total: 42.4s)Debug log

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