Average Error: 15.1 → 0.1
Time: 38.9s
Precision: 64
Internal Precision: 896
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\sqrt[3]{-1}}{\frac{1 + x}{\sqrt[3]{-1}}} \cdot \frac{\sqrt[3]{-1}}{x}\]

Error

Bits error versus x

Derivation

  1. Initial program 15.1

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  2. Using strategy rm

  3. Applied frac-sub14.4

    \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot x}}\]

  4. Applied simplify14.4

    \[\leadsto \frac{\color{blue}{x - \left(x + 1\right)}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt14.4

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - \left(x + 1\right)} \cdot \sqrt[3]{x - \left(x + 1\right)}\right) \cdot \sqrt[3]{x - \left(x + 1\right)}}}{\left(x + 1\right) \cdot x}\]

  7. Applied times-frac14.4

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x - \left(x + 1\right)} \cdot \sqrt[3]{x - \left(x + 1\right)}}{x + 1} \cdot \frac{\sqrt[3]{x - \left(x + 1\right)}}{x}}\]

  8. Applied simplify14.4

    \[\leadsto \color{blue}{\frac{\sqrt[3]{-1}}{\frac{1 + x}{\sqrt[3]{-1}}}} \cdot \frac{\sqrt[3]{x - \left(x + 1\right)}}{x}\]

  9. Applied simplify0.1

    \[\leadsto \frac{\sqrt[3]{-1}}{\frac{1 + x}{\sqrt[3]{-1}}} \cdot \color{blue}{\frac{\sqrt[3]{0 - 1}}{x}}\]

  10. Applied simplify0.1

    \[\leadsto \frac{\sqrt[3]{-1}}{\frac{1 + x}{\sqrt[3]{-1}}} \cdot \frac{\color{blue}{\sqrt[3]{-1}}}{x}\]

Runtime

Time bar (total: 38.9s)Debug logProfile

herbie shell --seed '#(1070131407 1246090267 3027482374 2150728003 2026520792 2347815650)' 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))