Average Error: 0.4 → 0.4
Time: 3.4s
Precision: binary64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{1}{x \cdot 9}\right) + \left(3 \cdot \sqrt{x}\right) \cdot \left(-1\right)\]

Error

Bits error versus x

Bits error versus y

Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\left(y + \frac{1}{x \cdot 9}\right) + \left(-1\right)\right)}\]

  4. Applied distribute-lft-in0.4

    \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{1}{x \cdot 9}\right) + \left(3 \cdot \sqrt{x}\right) \cdot \left(-1\right)}\]

  5. Final simplification0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{1}{x \cdot 9}\right) + \left(3 \cdot \sqrt{x}\right) \cdot \left(-1\right)\]

Reproduce

herbie shell --seed 2020163 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :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)))