math.cube on complex, real part

Average Error: 7.4 → 0.2

Time: 2.6s

Precision: binary64

Math

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↓

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Error

Bits error versus x.re

Bits error versus x.im

Target

Original	7.4
Target	0.2
Herbie	0.2

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Derivation

1. Initial program 7.4

   \[\]
2. Using strategy rm

3. Applied difference-of-squares 7.4

   \[\leadsto \]

4. Applied associate-*l* 0.2

   \[\leadsto \]

5. Simplified 0.2

   \[\leadsto \]
6. Using strategy rm

7. Applied sub-neg 0.2

   \[\leadsto \]

8. Applied distribute-lft-in 0.2

   \[\leadsto \]

9. Applied distribute-lft-in 0.3

   \[\leadsto \]

10. Applied associate--l+ 0.3

    \[\leadsto \]

11. Simplified 0.2

    \[\leadsto \]

12. Final simplification 0.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3.0 x.im))))

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