Average Error: 0.4 → 0.4

Time: 56.4s

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

The X axis uses an exponential scale — Bits error versus `x`

Target

Original	0.4
Target	0.4
Herbie	0.4

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

Derivation

Initial program 0.4
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
Taylor expanded around 0 0.4
\[\leadsto \left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{0.1111111111111111}{x}}\right) - 1.0\right)\]
Removed slow pow expressions.

Runtime

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)))