Error

Target

Derivation

1. Initial program 44.8

   \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
2. Using strategy rm

3. Applied add-cube-cbrt45.4

   \[\leadsto (x \cdot y + z)_* - \left(1 + \color{blue}{\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \sqrt[3]{x \cdot y + z}}\right)\]
4. Using strategy rm

5. Applied add-cube-cbrt45.3

   \[\leadsto (x \cdot y + z)_* - \left(1 + \left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \sqrt[3]{x \cdot y + z}}}\right)\]

6. Applied cbrt-prod45.4

   \[\leadsto (x \cdot y + z)_* - \left(1 + \left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}} \cdot \sqrt[3]{\sqrt[3]{x \cdot y + z}}\right)}\right)\]

7. Taylor expanded around -inf 59.3

   \[\leadsto \color{blue}{(x \cdot y + z)_* - \left(e^{\frac{-1}{9} \cdot \left(\log \left(\frac{-1}{x}\right) + \log \left(\frac{-1}{y}\right)\right)} \cdot e^{\frac{-8}{9} \cdot \left(\log \left(\frac{-1}{x}\right) + \log \left(\frac{-1}{y}\right)\right)} + 1\right)}\]

8. Applied simplify37.1

   \[\leadsto \color{blue}{\left((x \cdot y + z)_* - {\left(\frac{-1}{x} \cdot \frac{-1}{y}\right)}^{\left(\frac{-8}{9} + \frac{-1}{9}\right)}\right) - 1}\]

9. Taylor expanded around 0 59.1

   \[\leadsto \color{blue}{\left((x \cdot y + z)_* - e^{\log y + \log x}\right)} - 1\]

10. Applied simplify30.2

    \[\leadsto \color{blue}{\left((x \cdot y + z)_* - y \cdot x\right) - 1}\]

Runtime

Time bar (total: 35.5s)Debug logProfile

herbie shell --seed '#(1070258749 1877548225 2229079127 1588002776 3179087814 1886870650)' 
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

  (- (fma x y z) (+ 1 (+ (* x y) z))))