Average Error: 0.0 → 0.0
Time: 14.8s
Precision: 64
$\left(\frac{b}{a} \le 3.898171832519375494306393390829904773676 \cdot 10^{-17} \land b \le 6.123233995736766035868820147291983023128 \cdot 10^{-17}\right) \land b \ge 6.123233995736766035868820147291983023128 \cdot 10^{-17}$
$\frac{1}{\frac{1 - a \cdot b}{a + b}}$
$\frac{1}{\frac{1}{a + b} - \frac{a \cdot b}{a + b}}$
\frac{1}{\frac{1 - a \cdot b}{a + b}}
\frac{1}{\frac{1}{a + b} - \frac{a \cdot b}{a + b}}
double f(double a, double b) {
double r2345412 = 1.0;
double r2345413 = a;
double r2345414 = b;
double r2345415 = r2345413 * r2345414;
double r2345416 = r2345412 - r2345415;
double r2345417 = r2345413 + r2345414;
double r2345418 = r2345416 / r2345417;
double r2345419 = r2345412 / r2345418;
return r2345419;
}


double f(double a, double b) {
double r2345420 = 1.0;
double r2345421 = a;
double r2345422 = b;
double r2345423 = r2345421 + r2345422;
double r2345424 = r2345420 / r2345423;
double r2345425 = r2345421 * r2345422;
double r2345426 = r2345425 / r2345423;
double r2345427 = r2345424 - r2345426;
double r2345428 = r2345420 / r2345427;
return r2345428;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$\frac{1}{\frac{1 - a \cdot b}{a + b}}$
2. Using strategy rm
3. Applied div-sub0.0

$\leadsto \frac{1}{\color{blue}{\frac{1}{a + b} - \frac{a \cdot b}{a + b}}}$
4. Final simplification0.0

$\leadsto \frac{1}{\frac{1}{a + b} - \frac{a \cdot b}{a + b}}$

# Reproduce

herbie shell --seed 1
(FPCore (a b)
:name "1/((1-a*b)/(a+b))"
:precision binary64
:pre (and (and (<= (/ b a) 3.89817183251937549e-17) (<= b 6.12323399573676604e-17)) (>= b 6.12323399573676604e-17))
(/ 1 (/ (- 1 (* a b)) (+ a b))))