Average Error: 0.1 → 0.1
Time: 10.4s
Precision: 64
$\sqrt{\sqrt{x} + \log x}$
$\sqrt{\left(\sqrt{x} + \log \left(\sqrt{x}\right)\right) + \log \left(\sqrt{x}\right)}$
\sqrt{\sqrt{x} + \log x}
\sqrt{\left(\sqrt{x} + \log \left(\sqrt{x}\right)\right) + \log \left(\sqrt{x}\right)}
double f(double x) {
double r1453562 = x;
double r1453563 = sqrt(r1453562);
double r1453564 = log(r1453562);
double r1453565 = r1453563 + r1453564;
double r1453566 = sqrt(r1453565);
return r1453566;
}

double f(double x) {
double r1453567 = x;
double r1453568 = sqrt(r1453567);
double r1453569 = log(r1453568);
double r1453570 = r1453568 + r1453569;
double r1453571 = r1453570 + r1453569;
double r1453572 = sqrt(r1453571);
return r1453572;
}

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.1

$\sqrt{\sqrt{x} + \log x}$
2. Using strategy rm

$\leadsto \sqrt{\sqrt{x} + \log \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}}$
4. Applied log-prod0.1

$\leadsto \sqrt{\sqrt{x} + \color{blue}{\left(\log \left(\sqrt{x}\right) + \log \left(\sqrt{x}\right)\right)}}$
5. Applied associate-+r+0.1

$\leadsto \sqrt{\color{blue}{\left(\sqrt{x} + \log \left(\sqrt{x}\right)\right) + \log \left(\sqrt{x}\right)}}$
6. Final simplification0.1

$\leadsto \sqrt{\left(\sqrt{x} + \log \left(\sqrt{x}\right)\right) + \log \left(\sqrt{x}\right)}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "sqrt(sqrt(x)+log(x))"
:precision binary64
(sqrt (+ (sqrt x) (log x))))