Average Error: 0.4 → 0.4
Time: 47.2s
Precision: 64
Internal Precision: 384
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\]

Error

Bits error versus x

Bits error versus y

Target

Original0.4
Target0.4
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. Taylor expanded around 0 0.4

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

Runtime

Time bar (total: 47.2s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(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)))