Average Error: 7.0 → 0.2
Time: 1.1m
Precision: 64
Internal Precision: 320
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[3 \cdot \left(x.re \cdot \left(x.re \cdot x.im\right)\right) - {x.im}^{3}\]

Error

Bits error versus x.re

Bits error versus x.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.0
Target0.2
Herbie0.2
\[\left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.0

    \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]

  2. Applied simplify7.0

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

  3. Taylor expanded around 0 6.9

    \[\leadsto \color{blue}{3 \cdot \left({x.re}^{2} \cdot x.im\right) - {x.im}^{3}}\]
  4. Using strategy rm

  5. Applied unpow26.9

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

  6. Applied associate-*l*0.2

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018208 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"

  :herbie-target
  (+ (* (* x.re x.im) (* 2 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im)))

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