Rosa's Benchmark

Average Error: 0.2 → 0.1

Time: 1.7s

Precision: binary64

Math

\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

↓

\[x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)\]

FPCore

(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

↓

(FPCore (x)
 :precision binary64
 (* x (- 0.954929658551372 (* 0.12900613773279798 (* x x)))))

C

double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}

↓

double code(double x) {
	return x * (0.954929658551372 - (0.12900613773279798 * (x * x)));
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

2. Simplified 0.1

   \[\leadsto \color{blue}{0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}}\]
3. Using strategy rm

4. Applied unpow3_binary64 0.2

   \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \color{blue}{\left(\left(x \cdot x\right) \cdot x\right)}\]

5. Applied associate-*r*_binary64 0.1

   \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x}\]
6. Using strategy rm

7. Applied distribute-rgt-out--_binary64 0.1

   \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)}\]

8. Final simplification 0.1

   \[\leadsto x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)\]

Reproduce

herbie shell --seed 2020233 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))