Average Error: 0.5 → 0.0
Time: 11.0s
Precision: 64
$\cos \left(x + 1\right) \cdot 3 + x$
$\left(3 \cdot \sqrt[3]{\cos \left(x + 1\right)}\right) \cdot \left(\sqrt[3]{\cos \left(x + 1\right)} \cdot \sqrt[3]{\cos \left(x + 1\right)}\right) + x$
\cos \left(x + 1\right) \cdot 3 + x
\left(3 \cdot \sqrt[3]{\cos \left(x + 1\right)}\right) \cdot \left(\sqrt[3]{\cos \left(x + 1\right)} \cdot \sqrt[3]{\cos \left(x + 1\right)}\right) + x
double f(double x) {
double r333257 = x;
double r333258 = 1.0;
double r333259 = r333257 + r333258;
double r333260 = cos(r333259);
double r333261 = 3.0;
double r333262 = r333260 * r333261;
double r333263 = r333262 + r333257;
return r333263;
}


double f(double x) {
double r333264 = 3.0;
double r333265 = x;
double r333266 = 1.0;
double r333267 = r333265 + r333266;
double r333268 = cos(r333267);
double r333269 = cbrt(r333268);
double r333270 = r333264 * r333269;
double r333271 = r333269 * r333269;
double r333272 = r333270 * r333271;
double r333273 = r333272 + r333265;
return r333273;
}



Try it out

Results

 In Out
Enter valid numbers for all inputs

Derivation

1. Initial program 0.5

$\cos \left(x + 1\right) \cdot 3 + x$
2. Using strategy rm

$\leadsto \color{blue}{\left(\left(\sqrt[3]{\cos \left(x + 1\right)} \cdot \sqrt[3]{\cos \left(x + 1\right)}\right) \cdot \sqrt[3]{\cos \left(x + 1\right)}\right)} \cdot 3 + x$
4. Applied associate-*l*0.0

$\leadsto \color{blue}{\left(\sqrt[3]{\cos \left(x + 1\right)} \cdot \sqrt[3]{\cos \left(x + 1\right)}\right) \cdot \left(\sqrt[3]{\cos \left(x + 1\right)} \cdot 3\right)} + x$
5. Final simplification0.0

$\leadsto \left(3 \cdot \sqrt[3]{\cos \left(x + 1\right)}\right) \cdot \left(\sqrt[3]{\cos \left(x + 1\right)} \cdot \sqrt[3]{\cos \left(x + 1\right)}\right) + x$

Reproduce

herbie shell --seed 1
(FPCore (x)
:name "cos(x+1)*3+x"
(+ (* (cos (+ x 1)) 3) x))