Average Error: 6.5 → 0.2
Time: 16.3s
Precision: 64
$\frac{1}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)$
$\frac{1 \cdot d}{a} - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)$
\frac{1}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)
\frac{1 \cdot d}{a} - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)
double f(double a, double d, double bc) {
double r3058250 = 1.0;
double r3058251 = a;
double r3058252 = r3058250 / r3058251;
double r3058253 = d;
double r3058254 = r3058252 * r3058253;
double r3058255 = 0.3333333432674408;
double r3058256 = 2.0;
double r3058257 = pow(r3058251, r3058256);
double r3058258 = r3058250 / r3058257;
double r3058259 = bc;
double r3058260 = r3058258 * r3058259;
double r3058261 = r3058255 * r3058260;
double r3058262 = r3058254 - r3058261;
return r3058262;
}


double f(double a, double d, double bc) {
double r3058263 = 1.0;
double r3058264 = d;
double r3058265 = r3058263 * r3058264;
double r3058266 = a;
double r3058267 = r3058265 / r3058266;
double r3058268 = 0.3333333432674408;
double r3058269 = 1.0;
double r3058270 = 2.0;
double r3058271 = 2.0;
double r3058272 = r3058270 / r3058271;
double r3058273 = pow(r3058266, r3058272);
double r3058274 = r3058269 / r3058273;
double r3058275 = r3058263 / r3058273;
double r3058276 = bc;
double r3058277 = r3058275 * r3058276;
double r3058278 = r3058274 * r3058277;
double r3058279 = r3058268 * r3058278;
double r3058280 = r3058267 - r3058279;
return r3058280;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 6.5

$\frac{1}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)$
2. Using strategy rm
3. Applied sqr-pow6.5

$\leadsto \frac{1}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{\color{blue}{{a}^{\left(\frac{2}{2}\right)} \cdot {a}^{\left(\frac{2}{2}\right)}}} \cdot bc\right)$
4. Applied *-un-lft-identity6.5

$\leadsto \frac{1}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{\color{blue}{1 \cdot 1}}{{a}^{\left(\frac{2}{2}\right)} \cdot {a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)$
5. Applied times-frac6.4

$\leadsto \frac{1}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\color{blue}{\left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot \frac{1}{{a}^{\left(\frac{2}{2}\right)}}\right)} \cdot bc\right)$
6. Applied associate-*l*0.4

$\leadsto \frac{1}{a} \cdot d - 0.3333333432674407958984375 \cdot \color{blue}{\left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)}$
7. Using strategy rm
8. Applied associate-*l/0.2

$\leadsto \color{blue}{\frac{1 \cdot d}{a}} - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)$
9. Final simplification0.2

$\leadsto \frac{1 \cdot d}{a} - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)$

# Reproduce

herbie shell --seed 1
(FPCore (a d bc)
:name "(1/a*d)-0.3333333432674407958984375*(1/a^2*bc)"
:precision binary64
(- (* (/ 1 a) d) (* 0.333333343 (* (/ 1 (pow a 2)) bc))))