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;
}

Error

Bits error versus a

Bits error versus d

Bits error versus bc

Try it out

Your Program's Arguments

Results

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))))