Error

Target

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 add-sqr-sqrt0.7

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

4. Applied associate-*r*0.7

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

6. Applied associate--l+0.7

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

7. Applied distribute-lft-in0.7

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

8. Applied simplify0.6

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

9. Applied simplify0.4

   \[\leadsto \sqrt{x} \cdot \left(3.0 \cdot y\right) + \color{blue}{\left(\frac{\frac{1.0}{x}}{9.0} - 1.0\right) \cdot \left(\sqrt{x} \cdot 3.0\right)}\]
10. Removed slow pow expressions.

Runtime

Time bar (total: 1.7m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-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)))