Error

Target

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 prod-diff6.8

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

4. Simplified0.1

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

5. Simplified0.1

   \[\leadsto (\left(x.re \cdot \left(x.im + x.im\right)\right) \cdot \left(-x.im\right) + \left((\left(x.re \cdot x.im\right) \cdot \left(-x.im\right) + \left({x.re}^{3}\right))_*\right))_* + \color{blue}{0}\]

6. Final simplification0.1

   \[\leadsto (\left(x.re \cdot \left(x.im + x.im\right)\right) \cdot \left(-x.im\right) + \left((\left(x.re \cdot x.im\right) \cdot \left(-x.im\right) + \left({x.re}^{3}\right))_*\right))_*\]

Runtime

Time bar (total: 29.4s)Debug logProfile

herbie shell --seed 2018217 +o rules:numerics
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"

  :herbie-target
  (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3 x.im))))

  (- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im)))