Average Error: 0.4 → 0.4
Time: 44.4s
Precision: 64
Internal precision: 128
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
⬇
\[3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right)\]

Error

Bits error versus x

Bits error versus y

Target

Original0.4
Comparison0.4
Herbie0.4
\[ 3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right) \]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l* 0.4

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

  4. Applied taylor 0.4

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

  5. Taylor expanded around 0 0.4

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

Runtime

Time bar (total: 44.4s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(4184523614 803327860 563030331 1536604562 2705245453 1824711563)'
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

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

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