Average Error: 24.1 → 24.2
Time: 13.0s
Precision: 64
${\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}$
$\log \left(\sqrt[3]{{\left(e^{{\left(\sin x\right)}^{2}}\right)}^{3}}\right) + {\left(\cos x\right)}^{2}$
{\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}
\log \left(\sqrt[3]{{\left(e^{{\left(\sin x\right)}^{2}}\right)}^{3}}\right) + {\left(\cos x\right)}^{2}
double f(double x) {
double r783082 = x;
double r783083 = sin(r783082);
double r783084 = 2.0;
double r783085 = pow(r783083, r783084);
double r783086 = cos(r783082);
double r783087 = pow(r783086, r783084);
double r783088 = r783085 + r783087;
return r783088;
}

double f(double x) {
double r783089 = x;
double r783090 = sin(r783089);
double r783091 = 2.0;
double r783092 = pow(r783090, r783091);
double r783093 = exp(r783092);
double r783094 = 3.0;
double r783095 = pow(r783093, r783094);
double r783096 = cbrt(r783095);
double r783097 = log(r783096);
double r783098 = cos(r783089);
double r783099 = pow(r783098, r783091);
double r783100 = r783097 + r783099;
return r783100;
}

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 24.1

${\left(\sin x\right)}^{2} + {\left(\cos x\right)}^{2}$
2. Using strategy rm

$\leadsto \color{blue}{\log \left(e^{{\left(\sin x\right)}^{2}}\right)} + {\left(\cos x\right)}^{2}$
4. Using strategy rm

$\leadsto \log \color{blue}{\left(\sqrt[3]{\left(e^{{\left(\sin x\right)}^{2}} \cdot e^{{\left(\sin x\right)}^{2}}\right) \cdot e^{{\left(\sin x\right)}^{2}}}\right)} + {\left(\cos x\right)}^{2}$
6. Simplified24.2

$\leadsto \log \left(\sqrt[3]{\color{blue}{{\left(e^{{\left(\sin x\right)}^{2}}\right)}^{3}}}\right) + {\left(\cos x\right)}^{2}$
7. Final simplification24.2

$\leadsto \log \left(\sqrt[3]{{\left(e^{{\left(\sin x\right)}^{2}}\right)}^{3}}\right) + {\left(\cos x\right)}^{2}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "sin(x)^2+cos(x)^2"
:precision binary64
(+ (pow (sin x) 2) (pow (cos x) 2)))