Average Error: 7.3 → 0.3
Time: 14.9s
Precision: 64
\[\frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)\]
\[\frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \frac{\frac{1 \cdot bc}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}\]
\frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)
\frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \frac{\frac{1 \cdot bc}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}
double f(double d, double a, double bc) {
        double r3077580 = d;
        double r3077581 = a;
        double r3077582 = r3077580 / r3077581;
        double r3077583 = r3077582 * r3077580;
        double r3077584 = 0.3333333432674408;
        double r3077585 = 1.0;
        double r3077586 = 2.0;
        double r3077587 = pow(r3077581, r3077586);
        double r3077588 = r3077585 / r3077587;
        double r3077589 = bc;
        double r3077590 = r3077588 * r3077589;
        double r3077591 = r3077584 * r3077590;
        double r3077592 = r3077583 - r3077591;
        return r3077592;
}

double f(double d, double a, double bc) {
        double r3077593 = d;
        double r3077594 = a;
        double r3077595 = r3077593 / r3077594;
        double r3077596 = r3077595 * r3077593;
        double r3077597 = 0.3333333432674408;
        double r3077598 = 1.0;
        double r3077599 = bc;
        double r3077600 = r3077598 * r3077599;
        double r3077601 = 2.0;
        double r3077602 = 2.0;
        double r3077603 = r3077601 / r3077602;
        double r3077604 = pow(r3077594, r3077603);
        double r3077605 = r3077600 / r3077604;
        double r3077606 = r3077605 / r3077604;
        double r3077607 = r3077597 * r3077606;
        double r3077608 = r3077596 - r3077607;
        return r3077608;
}

Error

Bits error versus d

Bits error versus a

Bits error versus bc

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 7.3

    \[\frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)\]
  2. Using strategy rm
  3. Applied sqr-pow7.3

    \[\leadsto \frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{\color{blue}{{a}^{\left(\frac{2}{2}\right)} \cdot {a}^{\left(\frac{2}{2}\right)}}} \cdot bc\right)\]
  4. Applied *-un-lft-identity7.3

    \[\leadsto \frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{\color{blue}{1 \cdot 1}}{{a}^{\left(\frac{2}{2}\right)} \cdot {a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\]
  5. Applied times-frac7.2

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

    \[\leadsto \frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \color{blue}{\left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)}\]
  7. Using strategy rm
  8. Applied *-un-lft-identity0.4

    \[\leadsto \frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{1}{\color{blue}{1 \cdot {a}^{\left(\frac{2}{2}\right)}}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)\]
  9. Applied add-sqr-sqrt0.4

    \[\leadsto \frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{1 \cdot {a}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)\]
  10. Applied times-frac0.4

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

    \[\leadsto \frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \color{blue}{\left(\frac{\sqrt{1}}{1} \cdot \left(\frac{\sqrt{1}}{{a}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{1}{{a}^{\left(\frac{2}{2}\right)}} \cdot bc\right)\right)\right)}\]
  12. Simplified0.3

    \[\leadsto \frac{d}{a} \cdot d - 0.3333333432674407958984375 \cdot \left(\frac{\sqrt{1}}{1} \cdot \color{blue}{\frac{\frac{1 \cdot bc}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}}\right)\]
  13. Final simplification0.3

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

Reproduce

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