ENA, Section 1.4, Exercise 1

Percentage Accurate: 94.5% → 99.4%

Time: 10.1s

Alternatives: 6

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, 0.5× 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 95.4%

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

   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 95.4%

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

   4. associate-/l* 95.4%

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

   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 2: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot {\left({\left(e^{5}\right)}^{\left(x \cdot 2\right)}\right)}^{x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (pow (pow (exp 5.0) (* x 2.0)) x)))

C

double code(double x) {
	return cos(x) * pow(pow(exp(5.0), (x * 2.0)), x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * ((exp(5.0d0) ** (x * 2.0d0)) ** x)
end function

Java

public static double code(double x) {
	return Math.cos(x) * Math.pow(Math.pow(Math.exp(5.0), (x * 2.0)), x);
}

Python

def code(x):
	return math.cos(x) * math.pow(math.pow(math.exp(5.0), (x * 2.0)), x)

Julia

function code(x)
	return Float64(cos(x) * ((exp(5.0) ^ Float64(x * 2.0)) ^ x))
end

MATLAB

function tmp = code(x)
	tmp = cos(x) * ((exp(5.0) ^ (x * 2.0)) ^ x);
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Power[N[Power[N[Exp[5.0], $MachinePrecision], N[(x * 2.0), $MachinePrecision]], $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 95.4%

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

   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 95.4%

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

   4. prod-exp 95.4%

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

   5. metadata-eval 95.4%

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

   6. div-inv 95.4%

      \[\leadsto \cos x \cdot {\left(e^{20}\right)}^{\color{blue}{\left(\left(x \cdot x\right) \cdot \frac{1}{2}\right)}} \]

   7. pow2 95.4%

      \[\leadsto \cos x \cdot {\left(e^{20}\right)}^{\left(\color{blue}{{x}^{2}} \cdot \frac{1}{2}\right)} \]

   8. metadata-eval 95.4%

      \[\leadsto \cos x \cdot {\left(e^{20}\right)}^{\left({x}^{2} \cdot \color{blue}{0.5}\right)} \]

4. Applied egg-rr 95.4%

   \[\leadsto \cos x \cdot \color{blue}{{\left(e^{20}\right)}^{\left({x}^{2} \cdot 0.5\right)}} \]
5. Step-by-step derivation

   1. unpow2 95.4%

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

   2. associate-*r* 95.4%

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

   3. metadata-eval 95.4%

      \[\leadsto \cos x \cdot {\left(e^{20}\right)}^{\left(x \cdot \left(x \cdot \color{blue}{\frac{1}{2}}\right)\right)} \]

   4. div-inv 95.4%

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

   5. pow-pow 99.4%

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

   6. add-sqr-sqrt 99.0%

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

   7. unpow-prod-down 98.9%

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

   8. div-inv 98.9%

      \[\leadsto \cos x \cdot \left({\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\color{blue}{\left(x \cdot \frac{1}{2}\right)}} \cdot {\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\left(\frac{x}{2}\right)}\right) \]

   9. metadata-eval 98.9%

      \[\leadsto \cos x \cdot \left({\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\left(x \cdot \color{blue}{0.5}\right)} \cdot {\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\left(\frac{x}{2}\right)}\right) \]

   10. div-inv 98.9%

       \[\leadsto \cos x \cdot \left({\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\left(x \cdot 0.5\right)} \cdot {\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\color{blue}{\left(x \cdot \frac{1}{2}\right)}}\right) \]

   11. metadata-eval 98.9%

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

6. Applied egg-rr 98.9%

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

   1. pow-sqr 99.2%

      \[\leadsto \cos x \cdot \color{blue}{{\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\left(2 \cdot \left(x \cdot 0.5\right)\right)}} \]

   2. *-commutative 99.2%

      \[\leadsto \cos x \cdot {\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\left(2 \cdot \color{blue}{\left(0.5 \cdot x\right)}\right)} \]

   3. associate-*r* 99.2%

      \[\leadsto \cos x \cdot {\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}^{\color{blue}{\left(\left(2 \cdot 0.5\right) \cdot x\right)}} \]

   4. metadata-eval 99.2%

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

   5. *-lft-identity 99.2%

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

8. Simplified 99.2%

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

   1. sqrt-pow1 99.2%

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

   2. add-sqr-sqrt 98.1%

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

   3. unpow-prod-down 98.0%

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

   4. metadata-eval 98.0%

      \[\leadsto \cos x \cdot {\left({\left(\sqrt{e^{\color{blue}{10 + 10}}}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{20}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   5. prod-exp 98.0%

      \[\leadsto \cos x \cdot {\left({\left(\sqrt{\color{blue}{e^{10} \cdot e^{10}}}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{20}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   6. metadata-eval 98.0%

      \[\leadsto \cos x \cdot {\left({\left(\sqrt{e^{\color{blue}{3.3333333333333335 \cdot 3}} \cdot e^{10}}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{20}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   7. pow-exp 96.7%

      \[\leadsto \cos x \cdot {\left({\left(\sqrt{\color{blue}{{\left(e^{3.3333333333333335}\right)}^{3}} \cdot e^{10}}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{20}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   8. metadata-eval 96.7%

      \[\leadsto \cos x \cdot {\left({\left(\sqrt{{\left(e^{3.3333333333333335}\right)}^{3} \cdot e^{\color{blue}{3.3333333333333335 \cdot 3}}}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{20}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   9. pow-exp 95.2%

      \[\leadsto \cos x \cdot {\left({\left(\sqrt{{\left(e^{3.3333333333333335}\right)}^{3} \cdot \color{blue}{{\left(e^{3.3333333333333335}\right)}^{3}}}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{20}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   10. sqrt-unprod 94.7%

       \[\leadsto \cos x \cdot {\left({\color{blue}{\left(\sqrt{{\left(e^{3.3333333333333335}\right)}^{3}} \cdot \sqrt{{\left(e^{3.3333333333333335}\right)}^{3}}\right)}}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{20}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   11. add-sqr-sqrt 95.2%

       \[\leadsto \cos x \cdot {\left({\color{blue}{\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{20}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   12. metadata-eval 95.2%

       \[\leadsto \cos x \cdot {\left({\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{\color{blue}{10 + 10}}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   13. prod-exp 95.2%

       \[\leadsto \cos x \cdot {\left({\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{\color{blue}{e^{10} \cdot e^{10}}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   14. metadata-eval 95.2%

       \[\leadsto \cos x \cdot {\left({\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{e^{\color{blue}{3.3333333333333335 \cdot 3}} \cdot e^{10}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   15. pow-exp 94.7%

       \[\leadsto \cos x \cdot {\left({\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{\color{blue}{{\left(e^{3.3333333333333335}\right)}^{3}} \cdot e^{10}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   16. metadata-eval 94.7%

       \[\leadsto \cos x \cdot {\left({\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{{\left(e^{3.3333333333333335}\right)}^{3} \cdot e^{\color{blue}{3.3333333333333335 \cdot 3}}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   17. pow-exp 93.9%

       \[\leadsto \cos x \cdot {\left({\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}^{\left(\frac{x}{2}\right)} \cdot {\left(\sqrt{{\left(e^{3.3333333333333335}\right)}^{3} \cdot \color{blue}{{\left(e^{3.3333333333333335}\right)}^{3}}}\right)}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   18. sqrt-unprod 93.6%

       \[\leadsto \cos x \cdot {\left({\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}^{\left(\frac{x}{2}\right)} \cdot {\color{blue}{\left(\sqrt{{\left(e^{3.3333333333333335}\right)}^{3}} \cdot \sqrt{{\left(e^{3.3333333333333335}\right)}^{3}}\right)}}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

   19. add-sqr-sqrt 93.9%

       \[\leadsto \cos x \cdot {\left({\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}^{\left(\frac{x}{2}\right)} \cdot {\color{blue}{\left({\left(e^{3.3333333333333335}\right)}^{3}\right)}}^{\left(\frac{x}{2}\right)}\right)}^{x} \]

10. Applied egg-rr 98.1%

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

    1. pow-sqr 98.3%

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

    2. *-commutative 98.3%

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

12. Simplified 98.3%

    \[\leadsto \cos x \cdot {\color{blue}{\left({\left(e^{5}\right)}^{\left(x \cdot 2\right)}\right)}}^{x} \]
13. 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 95.4%

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

   2. pow-unpow 98.0%

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

4. Applied egg-rr 98.0%

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

Alternative 4: 95.3% 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 95.4%

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

3. Simplified 95.4%

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

Alternative 5: 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 6: 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 95.4%

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

   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 95.4%

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

   4. associate-/l* 95.4%

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

   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 2024145 
(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)))))