Input Error: 29.6b
Output Error: 29.6b
Time: 35.9s
Precision: 64b
Ground Truth: 128b
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
⬇
\[\sqrt[3]{{\left(\sqrt{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3}\right)}^2} - {x}^{\left(\frac{1}{3}\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 29.6b

    \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube 29.6b

    \[\leadsto \color{blue}{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3}} - {x}^{\left(\frac{1}{3}\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt 29.6b

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\sqrt{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3}\right)}^2}} - {x}^{\left(\frac{1}{3}\right)}\]
  6. Removed slow pow expressions

Runtime

Total time: 35.9s Debug log

herbie --seed '#(2862171413 1751114697 865772179 3574940685 1233564312 1256601581)'
(FPCore (x)
  :name "NMSE problem 3.3.4"
  (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3))))