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Derivation

1. Initial program 1.6

   \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm

3. Applied add-sqr-sqrt31.7

   \[\leadsto \left|\color{blue}{\sqrt{\frac{x + 4}{y}} \cdot \sqrt{\frac{x + 4}{y}}} - \frac{x}{y} \cdot z\right|\]

4. Applied prod-diff31.7

   \[\leadsto \left|\color{blue}{(\left(\sqrt{\frac{x + 4}{y}}\right) \cdot \left(\sqrt{\frac{x + 4}{y}}\right) + \left(-z \cdot \frac{x}{y}\right))_* + (\left(-z\right) \cdot \left(\frac{x}{y}\right) + \left(z \cdot \frac{x}{y}\right))_*}\right|\]

5. Simplified1.6

   \[\leadsto \left|\color{blue}{\left(\frac{4 + x}{y} - \frac{z}{\frac{y}{x}}\right)} + (\left(-z\right) \cdot \left(\frac{x}{y}\right) + \left(z \cdot \frac{x}{y}\right))_*\right|\]

6. Simplified1.7

   \[\leadsto \left|\left(\frac{4 + x}{y} - \frac{z}{\frac{y}{x}}\right) + \color{blue}{0}\right|\]

7. Final simplification1.7

   \[\leadsto \left|\frac{x + 4}{y} - \frac{z}{\frac{y}{x}}\right|\]

Runtime

Time bar (total: 21.9s)Debug logProfile

herbie shell --seed 2018242 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))