Average Error: 3.6 → 0.4
Time: 3.8s
Precision: binary64
\[1.99 \leq x \land x \leq 2.01\]
\[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
↓
\[\cos x \cdot {\left({\left(e^{20}\right)}^{x}\right)}^{\left(x \cdot 0.5\right)} \]
\cos x \cdot e^{10 \cdot \left(x \cdot x\right)}
↓
\cos x \cdot {\left({\left(e^{20}\right)}^{x}\right)}^{\left(x \cdot 0.5\right)}

(FPCore (x) :precision binary64 (* (cos x) (exp (* 10.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (* (cos x) (pow (pow (exp 20.0) x) (* x 0.5))))
double code(double x) {
	return cos(x) * exp((10.0 * (x * x)));
}
↓
double code(double x) {
	return cos(x) * pow(pow(exp(20.0), x), (x * 0.5));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.6

    \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]

  2. Applied egg-rr1.3

    \[\leadsto \cos x \cdot \color{blue}{{\left({\left(e^{10}\right)}^{x}\right)}^{x}} \]

  3. Applied egg-rr0.5

    \[\leadsto \cos x \cdot {\color{blue}{\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}}^{x} \]

  4. Applied egg-rr0.4

    \[\leadsto \cos x \cdot \color{blue}{\sqrt{{\left({\left(e^{20}\right)}^{x}\right)}^{x}}} \]

  5. Applied egg-rr0.4

    \[\leadsto \cos x \cdot \color{blue}{{\left({\left(e^{20}\right)}^{x}\right)}^{\left(\left(x \cdot 0.5\right) \cdot 1\right)}} \]

  6. Final simplification0.4

    \[\leadsto \cos x \cdot {\left({\left(e^{20}\right)}^{x}\right)}^{\left(x \cdot 0.5\right)} \]

Reproduce

herbie shell --seed 2022130 
(FPCore (x)
  :name "ENA, Section 1.4, Exercise 1"
  :precision binary64
  :pre (and (<= 1.99 x) (<= x 2.01))
  (* (cos x) (exp (* 10.0 (* x x)))))