Error

Derivation

1. Initial program 6.8

   \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
2. Using strategy rm

3. Applied difference-of-squares6.8

   \[\leadsto \color{blue}{\left(\left(x.re + x.im\right) \cdot \left(x.re - x.im\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]

4. Applied associate-*l*0.2

   \[\leadsto \color{blue}{\left(x.re + x.im\right) \cdot \left(\left(x.re - x.im\right) \cdot x.re\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
5. Using strategy rm

6. Applied add-cube-cbrt0.7

   \[\leadsto \left(x.re + x.im\right) \cdot \left(\color{blue}{\left(\left(\sqrt[3]{x.re - x.im} \cdot \sqrt[3]{x.re - x.im}\right) \cdot \sqrt[3]{x.re - x.im}\right)} \cdot x.re\right) - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]

7. Applied associate-*l*0.7

   \[\leadsto \left(x.re + x.im\right) \cdot \color{blue}{\left(\left(\sqrt[3]{x.re - x.im} \cdot \sqrt[3]{x.re - x.im}\right) \cdot \left(\sqrt[3]{x.re - x.im} \cdot x.re\right)\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]

Runtime

Time bar (total: 2.7m)Debug logProfile

herbie shell --seed '#(1070258749 1877548225 2229079127 1588002776 3179087814 1886870650)' 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  (- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im)))