Average Error: 0.3 → 0.1
Time: 23.2s
Precision: 64
Internal precision: 128
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
⬇
\[\left(1.0 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

Error

Bits error versus x

Bits error versus y

Target

Original0.3
Comparison0.3
Herbie0.1
\[ \left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}} \]

Derivation

  1. Initial program 0.3

    \[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]

  2. Applied taylor 0.2

    \[\leadsto \left(1.0 - 0.1111111111111111 \cdot \frac{1}{x}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]

  3. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(1.0 - 0.1111111111111111 \cdot \frac{1}{x}\right)} - \frac{y}{3.0 \cdot \sqrt{x}}\]

  4. Applied simplify 0.1

    \[\leadsto \color{blue}{\left(1.0 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}}\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 23.2s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1681455867 691908676 1588863763 2969522039 3657749612 1728352136)'
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

  :target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))