Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B

Average Error: 0.0 → 0.0

Time: 3.7s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x \cdot \left(1 - x \cdot 0.5\right)\]

↓

\[1 \cdot x + \left(-0.5 \cdot {x}^{2}\right)\]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[x \cdot \left(1 - x \cdot 0.5\right)\]
2. Using strategy rm

3. Applied sub-neg 0.0

   \[\leadsto x \cdot \color{blue}{\left(1 + \left(-x \cdot 0.5\right)\right)}\]

4. Applied distribute-lft-in 0.0

   \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)}\]

5. Simplified 0.0

   \[\leadsto \color{blue}{1 \cdot x} + x \cdot \left(-x \cdot 0.5\right)\]

6. Simplified 0.0

   \[\leadsto 1 \cdot x + \color{blue}{\left(-0.5 \cdot {x}^{2}\right)}\]

7. Final simplification 0.0

   \[\leadsto 1 \cdot x + \left(-0.5 \cdot {x}^{2}\right)\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1.0 (* x 0.5))))