Average Error: 0.3 → 0.1
Time: 25.6s
Precision: 64
$\frac{d}{a} - 0.3333333432674407958984375 \cdot \left(\frac{1}{a} \cdot \left(\frac{1}{a} \cdot bc\right)\right)$
$\frac{d}{a} - \frac{0.3333333432674407958984375 \cdot \frac{bc}{a}}{a}$
\frac{d}{a} - 0.3333333432674407958984375 \cdot \left(\frac{1}{a} \cdot \left(\frac{1}{a} \cdot bc\right)\right)
\frac{d}{a} - \frac{0.3333333432674407958984375 \cdot \frac{bc}{a}}{a}
double f(double d, double a, double bc) {
double r3082986 = d;
double r3082987 = a;
double r3082988 = r3082986 / r3082987;
double r3082989 = 0.3333333432674408;
double r3082990 = 1.0;
double r3082991 = r3082990 / r3082987;
double r3082992 = bc;
double r3082993 = r3082991 * r3082992;
double r3082994 = r3082991 * r3082993;
double r3082995 = r3082989 * r3082994;
double r3082996 = r3082988 - r3082995;
return r3082996;
}


double f(double d, double a, double bc) {
double r3082997 = d;
double r3082998 = a;
double r3082999 = r3082997 / r3082998;
double r3083000 = 0.3333333432674408;
double r3083001 = bc;
double r3083002 = r3083001 / r3082998;
double r3083003 = r3083000 * r3083002;
double r3083004 = r3083003 / r3082998;
double r3083005 = r3082999 - r3083004;
return r3083005;
}



Try it out

Results

 In Out
Enter valid numbers for all inputs

Derivation

1. Initial program 0.3

$\frac{d}{a} - 0.3333333432674407958984375 \cdot \left(\frac{1}{a} \cdot \left(\frac{1}{a} \cdot bc\right)\right)$
2. Using strategy rm
3. Applied associate-*l/0.2

$\leadsto \frac{d}{a} - 0.3333333432674407958984375 \cdot \left(\frac{1}{a} \cdot \color{blue}{\frac{1 \cdot bc}{a}}\right)$
4. Applied associate-*r/0.2

$\leadsto \frac{d}{a} - 0.3333333432674407958984375 \cdot \color{blue}{\frac{\frac{1}{a} \cdot \left(1 \cdot bc\right)}{a}}$
5. Applied associate-*r/0.2

$\leadsto \frac{d}{a} - \color{blue}{\frac{0.3333333432674407958984375 \cdot \left(\frac{1}{a} \cdot \left(1 \cdot bc\right)\right)}{a}}$
6. Taylor expanded around 0 0.1

$\leadsto \frac{d}{a} - \frac{\color{blue}{0.3333333432674407958984375 \cdot \frac{bc}{a}}}{a}$
7. Final simplification0.1

$\leadsto \frac{d}{a} - \frac{0.3333333432674407958984375 \cdot \frac{bc}{a}}{a}$

Reproduce

herbie shell --seed 1
(FPCore (d a bc)
:name "(d/a)-0.3333333432674407958984375*(1/a*(1/a*bc))"
:precision binary64
(- (/ d a) (* 0.333333343 (* (/ 1 a) (* (/ 1 a) bc)))))