ENA, Section 1.4, Exercise 1

Percentage Accurate: 94.5% → 99.1%

Time: 10.5s

Alternatives: 12

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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x} \cdot {\cos x}^{3}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (cbrt (* (pow (sqrt (pow (exp 60.0) x)) x) (pow (cos x) 3.0))))

C

double code(double x) {
	return cbrt((pow(sqrt(pow(exp(60.0), x)), x) * pow(cos(x), 3.0)));
}

Java

public static double code(double x) {
	return Math.cbrt((Math.pow(Math.sqrt(Math.pow(Math.exp(60.0), x)), x) * Math.pow(Math.cos(x), 3.0)));
}

Julia

function code(x)
	return cbrt(Float64((sqrt((exp(60.0) ^ x)) ^ x) * (cos(x) ^ 3.0)))
end

Wolfram

code[x_] := N[Power[N[(N[Power[N[Sqrt[N[Power[N[Exp[60.0], $MachinePrecision], x], $MachinePrecision]], $MachinePrecision], x], $MachinePrecision] * N[Power[N[Cos[x], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]

Derivation

1. Initial program 94.7%

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

   1. pow-exp 95.3%

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

   2. *-commutative 95.3%

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

   3. pow-exp 94.7%

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

   4. associate-*r* 94.5%

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

   5. add-log-exp 94.5%

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

   6. log-pow 94.5%

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

   7. pow-pow 95.0%

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

   8. add-exp-log 96.8%

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

   9. add-cbrt-cube 96.8%

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

   10. add-cbrt-cube 96.8%

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

   11. cbrt-unprod 96.8%

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

3. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x} \cdot {\cos x}^{3}}} \]
4. Step-by-step derivation

   1. add-sqr-sqrt 98.7%

      \[\leadsto \sqrt[3]{{\color{blue}{\left(\sqrt{{\left(e^{30}\right)}^{x}} \cdot \sqrt{{\left(e^{30}\right)}^{x}}\right)}}^{x} \cdot {\cos x}^{3}} \]

   2. sqrt-unprod 98.8%

      \[\leadsto \sqrt[3]{{\color{blue}{\left(\sqrt{{\left(e^{30}\right)}^{x} \cdot {\left(e^{30}\right)}^{x}}\right)}}^{x} \cdot {\cos x}^{3}} \]

   3. pow-prod-down 98.9%

      \[\leadsto \sqrt[3]{{\left(\sqrt{\color{blue}{{\left(e^{30} \cdot e^{30}\right)}^{x}}}\right)}^{x} \cdot {\cos x}^{3}} \]

   4. prod-exp 99.2%

      \[\leadsto \sqrt[3]{{\left(\sqrt{{\color{blue}{\left(e^{30 + 30}\right)}}^{x}}\right)}^{x} \cdot {\cos x}^{3}} \]

   5. metadata-eval 99.2%

      \[\leadsto \sqrt[3]{{\left(\sqrt{{\left(e^{\color{blue}{60}}\right)}^{x}}\right)}^{x} \cdot {\cos x}^{3}} \]

5. Applied egg-rr 99.2%

   \[\leadsto \sqrt[3]{{\color{blue}{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}}^{x} \cdot {\cos x}^{3}} \]

6. Final simplification 99.2%

   \[\leadsto \sqrt[3]{{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x} \cdot {\cos x}^{3}} \]

Alternative 2: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot \sqrt[3]{\sqrt{{\left({\left(e^{60}\right)}^{x}\right)}^{x}}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* (cos x) (cbrt (sqrt (pow (pow (exp 60.0) x) x)))))

C

double code(double x) {
	return cos(x) * cbrt(sqrt(pow(pow(exp(60.0), x), x)));
}

Java

public static double code(double x) {
	return Math.cos(x) * Math.cbrt(Math.sqrt(Math.pow(Math.pow(Math.exp(60.0), x), x)));
}

Julia

function code(x)
	return Float64(cos(x) * cbrt(sqrt(((exp(60.0) ^ x) ^ x))))
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Power[N[Sqrt[N[Power[N[Power[N[Exp[60.0], $MachinePrecision], x], $MachinePrecision], x], $MachinePrecision]], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

   1. pow-exp 95.3%

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

   2. *-commutative 95.3%

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

   3. pow-exp 94.7%

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

   4. associate-*r* 94.5%

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

   5. add-log-exp 94.5%

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

   6. log-pow 94.5%

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

   7. pow-pow 95.0%

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

   8. add-exp-log 96.8%

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

   9. add-cbrt-cube 96.8%

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

   10. add-cbrt-cube 96.8%

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

   11. cbrt-unprod 96.8%

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

3. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x} \cdot {\cos x}^{3}}} \]
4. Step-by-step derivation

   1. add-sqr-sqrt 98.7%

      \[\leadsto \sqrt[3]{{\color{blue}{\left(\sqrt{{\left(e^{30}\right)}^{x}} \cdot \sqrt{{\left(e^{30}\right)}^{x}}\right)}}^{x} \cdot {\cos x}^{3}} \]

   2. sqrt-unprod 98.8%

      \[\leadsto \sqrt[3]{{\color{blue}{\left(\sqrt{{\left(e^{30}\right)}^{x} \cdot {\left(e^{30}\right)}^{x}}\right)}}^{x} \cdot {\cos x}^{3}} \]

   3. pow-prod-down 98.9%

      \[\leadsto \sqrt[3]{{\left(\sqrt{\color{blue}{{\left(e^{30} \cdot e^{30}\right)}^{x}}}\right)}^{x} \cdot {\cos x}^{3}} \]

   4. prod-exp 99.2%

      \[\leadsto \sqrt[3]{{\left(\sqrt{{\color{blue}{\left(e^{30 + 30}\right)}}^{x}}\right)}^{x} \cdot {\cos x}^{3}} \]

   5. metadata-eval 99.2%

      \[\leadsto \sqrt[3]{{\left(\sqrt{{\left(e^{\color{blue}{60}}\right)}^{x}}\right)}^{x} \cdot {\cos x}^{3}} \]

5. Applied egg-rr 99.2%

   \[\leadsto \sqrt[3]{{\color{blue}{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}}^{x} \cdot {\cos x}^{3}} \]
6. Step-by-step derivation

   1. *-commutative 99.2%

      \[\leadsto \sqrt[3]{\color{blue}{{\cos x}^{3} \cdot {\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x}}} \]

   2. cbrt-prod 98.9%

      \[\leadsto \color{blue}{\sqrt[3]{{\cos x}^{3}} \cdot \sqrt[3]{{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x}}} \]

   3. rem-cbrt-cube 99.0%

      \[\leadsto \color{blue}{\cos x} \cdot \sqrt[3]{{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x}} \]

   4. add-sqr-sqrt 99.1%

      \[\leadsto \cos x \cdot \sqrt[3]{\color{blue}{\sqrt{{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x}} \cdot \sqrt{{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x}}}} \]

   5. sqrt-unprod 99.0%

      \[\leadsto \cos x \cdot \sqrt[3]{\color{blue}{\sqrt{{\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x} \cdot {\left(\sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x}}}} \]

   6. pow-prod-down 99.1%

      \[\leadsto \cos x \cdot \sqrt[3]{\sqrt{\color{blue}{{\left(\sqrt{{\left(e^{60}\right)}^{x}} \cdot \sqrt{{\left(e^{60}\right)}^{x}}\right)}^{x}}}} \]

   7. add-sqr-sqrt 99.1%

      \[\leadsto \cos x \cdot \sqrt[3]{\sqrt{{\color{blue}{\left({\left(e^{60}\right)}^{x}\right)}}^{x}}} \]

7. Applied egg-rr 99.1%

   \[\leadsto \color{blue}{\cos x \cdot \sqrt[3]{\sqrt{{\left({\left(e^{60}\right)}^{x}\right)}^{x}}}} \]

8. Final simplification 99.1%

   \[\leadsto \cos x \cdot \sqrt[3]{\sqrt{{\left({\left(e^{60}\right)}^{x}\right)}^{x}}} \]

Alternative 3: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\cos x \cdot 0.3333333333333333\right) \cdot \left(3 \cdot \sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* (* (cos x) 0.3333333333333333) (* 3.0 (cbrt (pow (pow (exp 30.0) x) x)))))

C

double code(double x) {
	return (cos(x) * 0.3333333333333333) * (3.0 * cbrt(pow(pow(exp(30.0), x), x)));
}

Java

public static double code(double x) {
	return (Math.cos(x) * 0.3333333333333333) * (3.0 * Math.cbrt(Math.pow(Math.pow(Math.exp(30.0), x), x)));
}

Julia

function code(x)
	return Float64(Float64(cos(x) * 0.3333333333333333) * Float64(3.0 * cbrt(((exp(30.0) ^ x) ^ x))))
end

Wolfram

code[x_] := N[(N[(N[Cos[x], $MachinePrecision] * 0.3333333333333333), $MachinePrecision] * N[(3.0 * N[Power[N[Power[N[Power[N[Exp[30.0], $MachinePrecision], x], $MachinePrecision], x], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

   1. pow-exp 95.3%

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

   2. *-commutative 95.3%

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

   3. pow-exp 94.7%

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

   4. associate-*r* 94.5%

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

   5. add-log-exp 94.5%

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

   6. log-pow 94.5%

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

   7. pow-pow 95.0%

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

   8. add-exp-log 96.8%

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

   9. add-cbrt-cube 96.8%

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

   10. add-cbrt-cube 96.8%

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

   11. cbrt-unprod 96.8%

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

3. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x} \cdot {\cos x}^{3}}} \]

4. Taylor expanded in x around inf 95.6%

   \[\leadsto \sqrt[3]{{\color{blue}{\left(e^{30 \cdot x}\right)}}^{x} \cdot {\cos x}^{3}} \]
5. Step-by-step derivation

   1. cbrt-prod 95.6%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \sqrt[3]{{\cos x}^{3}}} \]

   2. rem-cbrt-cube 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \color{blue}{\cos x} \]

   3. *-un-lft-identity 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \color{blue}{\left(1 \cdot \cos x\right)} \]

   4. metadata-eval 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \left(\color{blue}{\left(3 \cdot 0.3333333333333333\right)} \cdot \cos x\right) \]

   5. associate-*r* 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \cos x\right)\right)} \]

   6. associate-*r* 95.6%

      \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot 3\right) \cdot \left(0.3333333333333333 \cdot \cos x\right)} \]

   7. exp-prod 98.8%

      \[\leadsto \left(\sqrt[3]{{\color{blue}{\left({\left(e^{30}\right)}^{x}\right)}}^{x}} \cdot 3\right) \cdot \left(0.3333333333333333 \cdot \cos x\right) \]

   8. *-commutative 98.8%

      \[\leadsto \left(\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}} \cdot 3\right) \cdot \color{blue}{\left(\cos x \cdot 0.3333333333333333\right)} \]

6. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\left(\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}} \cdot 3\right) \cdot \left(\cos x \cdot 0.3333333333333333\right)} \]

7. Final simplification 98.8%

   \[\leadsto \left(\cos x \cdot 0.3333333333333333\right) \cdot \left(3 \cdot \sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}}\right) \]

Alternative 4: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}} \cdot \left(\cos x \cdot 0.3333333333333333\right)\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* 3.0 (* (cbrt (pow (pow (exp 30.0) x) x)) (* (cos x) 0.3333333333333333))))

C

double code(double x) {
	return 3.0 * (cbrt(pow(pow(exp(30.0), x), x)) * (cos(x) * 0.3333333333333333));
}

Java

public static double code(double x) {
	return 3.0 * (Math.cbrt(Math.pow(Math.pow(Math.exp(30.0), x), x)) * (Math.cos(x) * 0.3333333333333333));
}

Julia

function code(x)
	return Float64(3.0 * Float64(cbrt(((exp(30.0) ^ x) ^ x)) * Float64(cos(x) * 0.3333333333333333)))
end

Wolfram

code[x_] := N[(3.0 * N[(N[Power[N[Power[N[Power[N[Exp[30.0], $MachinePrecision], x], $MachinePrecision], x], $MachinePrecision], 1/3], $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

   1. pow-exp 95.3%

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

   2. *-commutative 95.3%

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

   3. pow-exp 94.7%

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

   4. associate-*r* 94.5%

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

   5. add-log-exp 94.5%

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

   6. log-pow 94.5%

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

   7. pow-pow 95.0%

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

   8. add-exp-log 96.8%

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

   9. add-cbrt-cube 96.8%

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

   10. add-cbrt-cube 96.8%

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

   11. cbrt-unprod 96.8%

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

3. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x} \cdot {\cos x}^{3}}} \]

4. Taylor expanded in x around inf 95.6%

   \[\leadsto \sqrt[3]{{\color{blue}{\left(e^{30 \cdot x}\right)}}^{x} \cdot {\cos x}^{3}} \]
5. Step-by-step derivation

   1. cbrt-prod 95.6%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \sqrt[3]{{\cos x}^{3}}} \]

   2. rem-cbrt-cube 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \color{blue}{\cos x} \]

   3. *-un-lft-identity 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \color{blue}{\left(1 \cdot \cos x\right)} \]

   4. metadata-eval 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \left(\color{blue}{\left(3 \cdot 0.3333333333333333\right)} \cdot \cos x\right) \]

   5. associate-*r* 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \cos x\right)\right)} \]

   6. *-commutative 95.6%

      \[\leadsto \sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \color{blue}{\left(\left(0.3333333333333333 \cdot \cos x\right) \cdot 3\right)} \]

   7. associate-*r* 95.6%

      \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(e^{30 \cdot x}\right)}^{x}} \cdot \left(0.3333333333333333 \cdot \cos x\right)\right) \cdot 3} \]

   8. exp-prod 98.9%

      \[\leadsto \left(\sqrt[3]{{\color{blue}{\left({\left(e^{30}\right)}^{x}\right)}}^{x}} \cdot \left(0.3333333333333333 \cdot \cos x\right)\right) \cdot 3 \]

   9. *-commutative 98.9%

      \[\leadsto \left(\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}} \cdot \color{blue}{\left(\cos x \cdot 0.3333333333333333\right)}\right) \cdot 3 \]

6. Applied egg-rr 98.9%

   \[\leadsto \color{blue}{\left(\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}} \cdot \left(\cos x \cdot 0.3333333333333333\right)\right) \cdot 3} \]

7. Final simplification 98.9%

   \[\leadsto 3 \cdot \left(\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}} \cdot \left(\cos x \cdot 0.3333333333333333\right)\right) \]

Alternative 5: 98.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot \sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (cos x) (cbrt (pow (pow (exp 30.0) x) x))))

C

double code(double x) {
	return cos(x) * cbrt(pow(pow(exp(30.0), x), x));
}

Java

public static double code(double x) {
	return Math.cos(x) * Math.cbrt(Math.pow(Math.pow(Math.exp(30.0), x), x));
}

Julia

function code(x)
	return Float64(cos(x) * cbrt(((exp(30.0) ^ x) ^ x)))
end

Wolfram

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Power[N[Power[N[Power[N[Exp[30.0], $MachinePrecision], x], $MachinePrecision], x], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

   1. associate-*r* 94.5%

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

   2. add-log-exp 94.5%

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

   3. log-pow 94.5%

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

   4. pow-pow 95.0%

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

   5. add-exp-log 96.8%

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

   6. add-cbrt-cube 96.8%

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

   7. add-exp-log 96.5%

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

   8. pow-pow 96.2%

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

   9. log-pow 96.3%

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

   10. add-log-exp 96.3%

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

   11. associate-*r* 96.5%

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

   12. pow-exp 96.9%

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

   13. *-commutative 96.9%

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

3. Applied egg-rr 98.8%

   \[\leadsto \cos x \cdot \color{blue}{\sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}}} \]

4. Final simplification 98.8%

   \[\leadsto \cos x \cdot \sqrt[3]{{\left({\left(e^{30}\right)}^{x}\right)}^{x}} \]

Alternative 6: 97.9% 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 94.7%

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

   1. associate-*r* 94.5%

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

   2. exp-prod 95.1%

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

   3. sqr-pow 95.0%

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

   4. sqr-pow 95.1%

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

   5. exp-prod 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 7: 95.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \left(3 \cdot \left(\cos x \cdot 0.3333333333333333\right)\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* (* 3.0 (* (cos x) 0.3333333333333333)) (pow (exp 10.0) (* x x))))

C

double code(double x) {
	return (3.0 * (cos(x) * 0.3333333333333333)) * pow(exp(10.0), (x * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (3.0d0 * (cos(x) * 0.3333333333333333d0)) * (exp(10.0d0) ** (x * x))
end function

Java

public static double code(double x) {
	return (3.0 * (Math.cos(x) * 0.3333333333333333)) * Math.pow(Math.exp(10.0), (x * x));
}

Python

def code(x):
	return (3.0 * (math.cos(x) * 0.3333333333333333)) * math.pow(math.exp(10.0), (x * x))

Julia

function code(x)
	return Float64(Float64(3.0 * Float64(cos(x) * 0.3333333333333333)) * (exp(10.0) ^ Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = (3.0 * (cos(x) * 0.3333333333333333)) * (exp(10.0) ^ (x * x));
end

Wolfram

code[x_] := N[(N[(3.0 * N[(N[Cos[x], $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision] * N[Power[N[Exp[10.0], $MachinePrecision], N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

   1. exp-prod 95.3%

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

3. Simplified 95.3%

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

   1. add-log-exp 95.3%

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

   2. add-cube-cbrt 95.3%

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

   3. log-prod 95.3%

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

5. Applied egg-rr 95.3%

   \[\leadsto \color{blue}{\left(\log \left(\sqrt[3]{e^{\cos x}} \cdot \sqrt[3]{e^{\cos x}}\right) + \log \left(\sqrt[3]{e^{\cos x}}\right)\right)} \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]
6. Step-by-step derivation

   1. log-prod 95.3%

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

   2. count-2 95.3%

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

   3. distribute-lft1-in 95.3%

      \[\leadsto \color{blue}{\left(\left(2 + 1\right) \cdot \log \left(\sqrt[3]{e^{\cos x}}\right)\right)} \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   4. metadata-eval 95.3%

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

7. Simplified 95.3%

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

8. Taylor expanded in x around inf 95.3%

   \[\leadsto \left(3 \cdot \color{blue}{\log \left({\left(e^{\cos x}\right)}^{0.3333333333333333}\right)}\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]
9. Step-by-step derivation

   1. log-pow 95.3%

      \[\leadsto \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\cos x}\right)\right)}\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

   2. rem-log-exp 95.3%

      \[\leadsto \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\cos x}\right)\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

10. Simplified 95.3%

    \[\leadsto \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \cos x\right)}\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

11. Final simplification 95.3%

    \[\leadsto \left(3 \cdot \left(\cos x \cdot 0.3333333333333333\right)\right) \cdot {\left(e^{10}\right)}^{\left(x \cdot x\right)} \]

Alternative 8: 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 94.7%

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

   1. exp-prod 95.3%

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

3. Simplified 95.3%

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

4. Final simplification 95.3%

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

Alternative 9: 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 94.7%

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

2. Final simplification 94.7%

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

Alternative 10: 18.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ e^{10 \cdot \left(x \cdot x\right)} \cdot \left(1 + \left(x \cdot x\right) \cdot -0.5\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* (exp (* 10.0 (* x x))) (+ 1.0 (* (* x x) -0.5))))

C

double code(double x) {
	return exp((10.0 * (x * x))) * (1.0 + ((x * x) * -0.5));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = exp((10.0d0 * (x * x))) * (1.0d0 + ((x * x) * (-0.5d0)))
end function

Java

public static double code(double x) {
	return Math.exp((10.0 * (x * x))) * (1.0 + ((x * x) * -0.5));
}

Python

def code(x):
	return math.exp((10.0 * (x * x))) * (1.0 + ((x * x) * -0.5))

Julia

function code(x)
	return Float64(exp(Float64(10.0 * Float64(x * x))) * Float64(1.0 + Float64(Float64(x * x) * -0.5)))
end

MATLAB

function tmp = code(x)
	tmp = exp((10.0 * (x * x))) * (1.0 + ((x * x) * -0.5));
end

Wolfram

code[x_] := N[(N[Exp[N[(10.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

2. Taylor expanded in x around 0 18.2%

   \[\leadsto \color{blue}{\left(1 + -0.5 \cdot {x}^{2}\right)} \cdot e^{10 \cdot \left(x \cdot x\right)} \]
3. Step-by-step derivation

   1. unpow2 9.7%

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

4. Simplified 18.2%

   \[\leadsto \color{blue}{\left(1 + -0.5 \cdot \left(x \cdot x\right)\right)} \cdot e^{10 \cdot \left(x \cdot x\right)} \]

5. Final simplification 18.2%

   \[\leadsto e^{10 \cdot \left(x \cdot x\right)} \cdot \left(1 + \left(x \cdot x\right) \cdot -0.5\right) \]

Alternative 11: 1.5% accurate, 29.6× speedup

Math

\[\begin{array}{l} \\ 1 + \left(x \cdot x\right) \cdot 9.5 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 1.0 (* (* x x) 9.5)))

C

double code(double x) {
	return 1.0 + ((x * x) * 9.5);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 + ((x * x) * 9.5d0)
end function

Java

public static double code(double x) {
	return 1.0 + ((x * x) * 9.5);
}

Python

def code(x):
	return 1.0 + ((x * x) * 9.5)

Julia

function code(x)
	return Float64(1.0 + Float64(Float64(x * x) * 9.5))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 + ((x * x) * 9.5);
end

Wolfram

code[x_] := N[(1.0 + N[(N[(x * x), $MachinePrecision] * 9.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

2. Taylor expanded in x around 0 1.5%

   \[\leadsto \color{blue}{1 + 9.5 \cdot {x}^{2}} \]
3. Step-by-step derivation

   1. unpow2 1.5%

      \[\leadsto 1 + 9.5 \cdot \color{blue}{\left(x \cdot x\right)} \]

4. Simplified 1.5%

   \[\leadsto \color{blue}{1 + 9.5 \cdot \left(x \cdot x\right)} \]

5. Final simplification 1.5%

   \[\leadsto 1 + \left(x \cdot x\right) \cdot 9.5 \]

Alternative 12: 9.7% accurate, 29.6× speedup

Math

\[\begin{array}{l} \\ 1 + \left(x \cdot x\right) \cdot -0.5 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 1.0 (* (* x x) -0.5)))

C

double code(double x) {
	return 1.0 + ((x * x) * -0.5);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 + ((x * x) * (-0.5d0))
end function

Java

public static double code(double x) {
	return 1.0 + ((x * x) * -0.5);
}

Python

def code(x):
	return 1.0 + ((x * x) * -0.5)

Julia

function code(x)
	return Float64(1.0 + Float64(Float64(x * x) * -0.5))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 + ((x * x) * -0.5);
end

Wolfram

code[x_] := N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

2. Taylor expanded in x around 0 9.6%

   \[\leadsto \cos x \cdot \color{blue}{1} \]

3. Taylor expanded in x around 0 9.7%

   \[\leadsto \color{blue}{\left(1 + -0.5 \cdot {x}^{2}\right)} \cdot 1 \]
4. Step-by-step derivation

   1. unpow2 9.7%

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

5. Simplified 9.7%

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

6. Final simplification 9.7%

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

Reproduce

herbie shell --seed 2023171 
(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)))))