ENA, Section 1.4, Exercise 1

Percentage Accurate: 94.5% → 99.4%

Time: 10.1s

Alternatives: 8

Speedup: 1.0×

Specification

\[1.99 \leq x \land x \leq 2.01\]

Math

\[\begin{array}{l} \\ \cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (exp (* 10.0 (* x x)))))

C

double code(double x) {
	return cos(x) * exp((10.0 * (x * x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * exp((10.0d0 * (x * x)))
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.exp((10.0 * (x * x)));
}

Python

def code(x):
	return math.cos(x) * math.exp((10.0 * (x * x)))

Julia

function code(x)
	return Float64(cos(x) * exp(Float64(10.0 * Float64(x * x))))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * exp((10.0 * (x * x)));
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Exp[N[(10.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (exp (* 10.0 (* x x)))))

C

double code(double x) {
	return cos(x) * exp((10.0 * (x * x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * exp((10.0d0 * (x * x)))
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.exp((10.0 * (x * x)));
}

Python

def code(x):
	return math.cos(x) * math.exp((10.0 * (x * x)))

Julia

function code(x)
	return Float64(cos(x) * exp(Float64(10.0 * Float64(x * x))))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * exp((10.0 * (x * x)));
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Exp[N[(10.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot \sqrt{{\left({\left(e^{20}\right)}^{x}\right)}^{x}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (sqrt (pow (pow (exp 20.0) x) x))))

C

double code(double x) {
	return cos(x) * sqrt(pow(pow(exp(20.0), x), x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * sqrt(((exp(20.0d0) ** x) ** x))
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.sqrt(Math.pow(Math.pow(Math.exp(20.0), x), x));
}

Python

def code(x):
	return math.cos(x) * math.sqrt(math.pow(math.pow(math.exp(20.0), x), x))

Julia

function code(x)
	return Float64(cos(x) * sqrt(((exp(20.0) ^ x) ^ x)))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * sqrt(((exp(20.0) ^ x) ^ x));
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Sqrt[N[Power[N[Power[N[Exp[20.0], $MachinePrecision], x], $MachinePrecision], x], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow-exp 95.5%

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

   2. sqr-pow 95.5%

      \[\leadsto \cos x \cdot \color{blue}{\left({\left(e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)} \cdot {\left(e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)}\right)} \]

   3. pow-prod-down 95.5%

      \[\leadsto \cos x \cdot \color{blue}{{\left(e^{10} \cdot e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)}} \]

   4. associate-/l* 95.5%

      \[\leadsto \cos x \cdot {\left(e^{10} \cdot e^{10}\right)}^{\color{blue}{\left(x \cdot \frac{x}{2}\right)}} \]

   5. pow-unpow 98.0%

      \[\leadsto \cos x \cdot \color{blue}{{\left({\left(e^{10} \cdot e^{10}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)}} \]

   6. prod-exp 99.4%

      \[\leadsto \cos x \cdot {\left({\color{blue}{\left(e^{10 + 10}\right)}}^{x}\right)}^{\left(\frac{x}{2}\right)} \]

   7. metadata-eval 99.4%

      \[\leadsto \cos x \cdot {\left({\left(e^{\color{blue}{20}}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)} \]

4. Applied egg-rr 99.4%

   \[\leadsto \cos x \cdot \color{blue}{{\left({\left(e^{20}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)}} \]

5. Taylor expanded in x around inf 94.2%

   \[\leadsto \color{blue}{\cos x \cdot e^{0.5 \cdot \left(x \cdot \log \left({\left(e^{20}\right)}^{x}\right)\right)}} \]
6. Step-by-step derivation

   1. *-commutative 94.2%

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

   2. exp-prod 94.2%

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

   3. unpow1/2 94.2%

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

   4. *-commutative 94.2%

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

   5. exp-to-pow 99.4%

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

7. Simplified 99.4%

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

Alternative 2: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot {\left({\left(e^{20}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (pow (pow (exp 20.0) x) (/ x 2.0))))

C

double code(double x) {
	return cos(x) * pow(pow(exp(20.0), x), (x / 2.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * ((exp(20.0d0) ** x) ** (x / 2.0d0))
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.pow(Math.pow(Math.exp(20.0), x), (x / 2.0));
}

Python

def code(x):
	return math.cos(x) * math.pow(math.pow(math.exp(20.0), x), (x / 2.0))

Julia

function code(x)
	return Float64(cos(x) * ((exp(20.0) ^ x) ^ Float64(x / 2.0)))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * ((exp(20.0) ^ x) ^ (x / 2.0));
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Power[N[Power[N[Exp[20.0], $MachinePrecision], x], $MachinePrecision], N[(x / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow-exp 95.5%

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

   2. sqr-pow 95.5%

      \[\leadsto \cos x \cdot \color{blue}{\left({\left(e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)} \cdot {\left(e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)}\right)} \]

   3. pow-prod-down 95.5%

      \[\leadsto \cos x \cdot \color{blue}{{\left(e^{10} \cdot e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)}} \]

   4. associate-/l* 95.5%

      \[\leadsto \cos x \cdot {\left(e^{10} \cdot e^{10}\right)}^{\color{blue}{\left(x \cdot \frac{x}{2}\right)}} \]

   5. pow-unpow 98.0%

      \[\leadsto \cos x \cdot \color{blue}{{\left({\left(e^{10} \cdot e^{10}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)}} \]

   6. prod-exp 99.4%

      \[\leadsto \cos x \cdot {\left({\color{blue}{\left(e^{10 + 10}\right)}}^{x}\right)}^{\left(\frac{x}{2}\right)} \]

   7. metadata-eval 99.4%

      \[\leadsto \cos x \cdot {\left({\left(e^{\color{blue}{20}}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)} \]

4. Applied egg-rr 99.4%

   \[\leadsto \cos x \cdot \color{blue}{{\left({\left(e^{20}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)}} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot {\left({\left(e^{10}\right)}^{x}\right)}^{x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (pow (pow (exp 10.0) x) x)))

C

double code(double x) {
	return cos(x) * pow(pow(exp(10.0), x), x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * ((exp(10.0d0) ** x) ** x)
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.pow(Math.pow(Math.exp(10.0), x), x);
}

Python

def code(x):
	return math.cos(x) * math.pow(math.pow(math.exp(10.0), x), x)

Julia

function code(x)
	return Float64(cos(x) * ((exp(10.0) ^ x) ^ x))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * ((exp(10.0) ^ x) ^ x);
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Power[N[Power[N[Exp[10.0], $MachinePrecision], x], $MachinePrecision], x], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow-exp 95.5%

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

   2. pow-unpow 97.9%

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

4. Applied egg-rr 97.9%

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

Alternative 4: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot {\left(e^{{x}^{2}}\right)}^{10} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (pow (exp (pow x 2.0)) 10.0)))

C

double code(double x) {
	return cos(x) * pow(exp(pow(x, 2.0)), 10.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * (exp((x ** 2.0d0)) ** 10.0d0)
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.pow(Math.exp(Math.pow(x, 2.0)), 10.0);
}

Python

def code(x):
	return math.cos(x) * math.pow(math.exp(math.pow(x, 2.0)), 10.0)

Julia

function code(x)
	return Float64(cos(x) * (exp((x ^ 2.0)) ^ 10.0))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * (exp((x ^ 2.0)) ^ 10.0);
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Power[N[Exp[N[Power[x, 2.0], $MachinePrecision]], $MachinePrecision], 10.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 94.4%

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

   2. exp-prod 95.5%

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

   3. pow2 95.5%

      \[\leadsto \cos x \cdot {\left(e^{\color{blue}{{x}^{2}}}\right)}^{10} \]

4. Applied egg-rr 95.5%

   \[\leadsto \cos x \cdot \color{blue}{{\left(e^{{x}^{2}}\right)}^{10}} \]
5. Add Preprocessing

Alternative 5: 95.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(1 + \left(\cos x + 1\right)\right) + -1\right) + -1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* (+ (+ (+ 1.0 (+ (cos x) 1.0)) -1.0) -1.0) (pow (exp 10.0) (* x x))))

C

double code(double x) {
	return (((1.0 + (cos(x) + 1.0)) + -1.0) + -1.0) * pow(exp(10.0), (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (((1.0d0 + (cos(x) + 1.0d0)) + (-1.0d0)) + (-1.0d0)) * (exp(10.0d0) ** (x * x))
end function

Java

public static double code(double x) {
	return (((1.0 + (Math.cos(x) + 1.0)) + -1.0) + -1.0) * Math.pow(Math.exp(10.0), (x * x));
}

Python

def code(x):
	return (((1.0 + (math.cos(x) + 1.0)) + -1.0) + -1.0) * math.pow(math.exp(10.0), (x * x))

Julia

function code(x)
	return Float64(Float64(Float64(Float64(1.0 + Float64(cos(x) + 1.0)) + -1.0) + -1.0) * (exp(10.0) ^ Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = (((1.0 + (cos(x) + 1.0)) + -1.0) + -1.0) * (exp(10.0) ^ (x * x));
end

Wolfram

code[x_] := N[(N[(N[(N[(1.0 + N[(N[Cos[x], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision] + -1.0), $MachinePrecision] * N[Power[N[Exp[10.0], $MachinePrecision], N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
2. Step-by-step derivation

   1. exp-prod 95.5%

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

3. Simplified 95.5%

   \[\leadsto \color{blue}{\cos x \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. expm1-log1p-u 95.5%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos x\right)\right)} \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   2. expm1-undefine 95.5%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\cos x\right)} - 1\right)} \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

6. Applied egg-rr 95.5%

   \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\cos x\right)} - 1\right)} \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]
7. Step-by-step derivation

   1. expm1-log1p-u 95.5%

      \[\leadsto \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\mathsf{log1p}\left(\cos x\right)}\right)\right)} - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   2. expm1-undefine 95.4%

      \[\leadsto \left(\color{blue}{\left(e^{\mathsf{log1p}\left(e^{\mathsf{log1p}\left(\cos x\right)}\right)} - 1\right)} - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   3. log1p-undefine 95.4%

      \[\leadsto \left(\left(e^{\color{blue}{\log \left(1 + e^{\mathsf{log1p}\left(\cos x\right)}\right)}} - 1\right) - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   4. +-commutative 95.4%

      \[\leadsto \left(\left(e^{\log \color{blue}{\left(e^{\mathsf{log1p}\left(\cos x\right)} + 1\right)}} - 1\right) - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   5. add-exp-log 95.4%

      \[\leadsto \left(\left(\color{blue}{\left(e^{\mathsf{log1p}\left(\cos x\right)} + 1\right)} - 1\right) - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   6. log1p-undefine 95.5%

      \[\leadsto \left(\left(\left(e^{\color{blue}{\log \left(1 + \cos x\right)}} + 1\right) - 1\right) - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   7. rem-exp-log 95.5%

      \[\leadsto \left(\left(\left(\color{blue}{\left(1 + \cos x\right)} + 1\right) - 1\right) - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   8. +-commutative 95.5%

      \[\leadsto \left(\left(\left(\color{blue}{\left(\cos x + 1\right)} + 1\right) - 1\right) - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

8. Applied egg-rr 95.5%

   \[\leadsto \left(\color{blue}{\left(\left(\left(\cos x + 1\right) + 1\right) - 1\right)} - 1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

9. Final simplification 95.5%

   \[\leadsto \left(\left(\left(1 + \left(\cos x + 1\right)\right) + -1\right) + -1\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]
10. Add Preprocessing

Alternative 6: 95.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (pow (exp 10.0) (* x x))))

C

double code(double x) {
	return cos(x) * pow(exp(10.0), (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * (exp(10.0d0) ** (x * x))
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.pow(Math.exp(10.0), (x * x));
}

Python

def code(x):
	return math.cos(x) * math.pow(math.exp(10.0), (x * x))

Julia

function code(x)
	return Float64(cos(x) * (exp(10.0) ^ Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * (exp(10.0) ^ (x * x));
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Power[N[Exp[10.0], $MachinePrecision], N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
2. Step-by-step derivation

   1. exp-prod 95.5%

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

3. Simplified 95.5%

   \[\leadsto \color{blue}{\cos x \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 7: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (exp (* 10.0 (* x x)))))

C

double code(double x) {
	return cos(x) * exp((10.0 * (x * x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * exp((10.0d0 * (x * x)))
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.exp((10.0 * (x * x)));
}

Python

def code(x):
	return math.cos(x) * math.exp((10.0 * (x * x)))

Julia

function code(x)
	return Float64(cos(x) * exp(Float64(10.0 * Float64(x * x))))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * exp((10.0 * (x * x)));
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Exp[N[(10.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 8: 1.5% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0
end function

Java

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

1. Initial program 94.4%

   \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow-exp 95.5%

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

   2. sqr-pow 95.5%

      \[\leadsto \cos x \cdot \color{blue}{\left({\left(e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)} \cdot {\left(e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)}\right)} \]

   3. pow-prod-down 95.5%

      \[\leadsto \cos x \cdot \color{blue}{{\left(e^{10} \cdot e^{10}\right)}^{\left(\frac{x \cdot x}{2}\right)}} \]

   4. associate-/l* 95.5%

      \[\leadsto \cos x \cdot {\left(e^{10} \cdot e^{10}\right)}^{\color{blue}{\left(x \cdot \frac{x}{2}\right)}} \]

   5. pow-unpow 98.0%

      \[\leadsto \cos x \cdot \color{blue}{{\left({\left(e^{10} \cdot e^{10}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)}} \]

   6. prod-exp 99.4%

      \[\leadsto \cos x \cdot {\left({\color{blue}{\left(e^{10 + 10}\right)}}^{x}\right)}^{\left(\frac{x}{2}\right)} \]

   7. metadata-eval 99.4%

      \[\leadsto \cos x \cdot {\left({\left(e^{\color{blue}{20}}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)} \]

4. Applied egg-rr 99.4%

   \[\leadsto \cos x \cdot \color{blue}{{\left({\left(e^{20}\right)}^{x}\right)}^{\left(\frac{x}{2}\right)}} \]

5. Taylor expanded in x around 0 1.5%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024156 
(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)))))