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

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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

$\leadsto \frac{a}{\color{blue}{\sqrt{b \cdot b + a \cdot \left(a + b\right)} \cdot \sqrt{b \cdot b + a \cdot \left(a + b\right)}}} \cdot \frac{a}{a - b}$
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))))