\[\left(\left(\left(x2 \cdot x5 + x3 \cdot x6\right) - x2 \cdot x3\right) - x5 \cdot x6\right) + x1 \cdot \left(\left(\left(\left(\left(\left(-x1\right) + x2\right) + x3\right) - x4\right) + x5\right) + x6\right)\]

↓

\[\left(\left(x2 - \left(x4 - x3\right)\right) + \left(\left(-x1\right) + \left(x5 + x6\right)\right)\right) \cdot x1 + \frac{\left({x3}^{3} - {x5}^{3}\right) \cdot \left(x6 \cdot x6 - x2 \cdot x2\right)}{\left(x3 \cdot x3 + \left(x3 + x5\right) \cdot x5\right) \cdot \left(x2 + x6\right)}\]

Error

The X axis uses an exponential scale — Bits error versus `x1`

Derivation

Initial program 0.6
\[\left(\left(\left(x2 \cdot x5 + x3 \cdot x6\right) - x2 \cdot x3\right) - x5 \cdot x6\right) + x1 \cdot \left(\left(\left(\left(\left(\left(-x1\right) + x2\right) + x3\right) - x4\right) + x5\right) + x6\right)\]
Applied simplify0.5
\[\leadsto \color{blue}{\left(\left(x2 - \left(x4 - x3\right)\right) + \left(\left(-x1\right) + \left(x5 + x6\right)\right)\right) \cdot x1 + \left(x3 - x5\right) \cdot \left(x6 - x2\right)}\]
Using strategy rm
Applied flip--0.5
\[\leadsto \left(\left(x2 - \left(x4 - x3\right)\right) + \left(\left(-x1\right) + \left(x5 + x6\right)\right)\right) \cdot x1 + \left(x3 - x5\right) \cdot \color{blue}{\frac{x6 \cdot x6 - x2 \cdot x2}{x6 + x2}}\]
Applied flip3--0.5
\[\leadsto \left(\left(x2 - \left(x4 - x3\right)\right) + \left(\left(-x1\right) + \left(x5 + x6\right)\right)\right) \cdot x1 + \color{blue}{\frac{{x3}^{3} - {x5}^{3}}{x3 \cdot x3 + \left(x5 \cdot x5 + x3 \cdot x5\right)}} \cdot \frac{x6 \cdot x6 - x2 \cdot x2}{x6 + x2}\]
Applied frac-times0.5
\[\leadsto \left(\left(x2 - \left(x4 - x3\right)\right) + \left(\left(-x1\right) + \left(x5 + x6\right)\right)\right) \cdot x1 + \color{blue}{\frac{\left({x3}^{3} - {x5}^{3}\right) \cdot \left(x6 \cdot x6 - x2 \cdot x2\right)}{\left(x3 \cdot x3 + \left(x5 \cdot x5 + x3 \cdot x5\right)\right) \cdot \left(x6 + x2\right)}}\]
Applied simplify0.5
\[\leadsto \left(\left(x2 - \left(x4 - x3\right)\right) + \left(\left(-x1\right) + \left(x5 + x6\right)\right)\right) \cdot x1 + \frac{\left({x3}^{3} - {x5}^{3}\right) \cdot \left(x6 \cdot x6 - x2 \cdot x2\right)}{\color{blue}{\left(x3 \cdot x3 + \left(x3 + x5\right) \cdot x5\right) \cdot \left(x2 + x6\right)}}\]

Runtime

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (x1 x2 x3 x4 x5 x6)
  :name "kepler0"
  :pre (and (<= 4 x1 6.36) (<= 4 x2 6.36) (<= 4 x3 6.36) (<= 4 x4 6.36) (<= 4 x5 6.36) (<= 4 x6 6.36))
  (+ (- (- (+ (* x2 x5) (* x3 x6)) (* x2 x3)) (* x5 x6)) (* x1 (+ (+ (- (+ (+ (- x1) x2) x3) x4) x5) x6))))