Average Error: 3.1 → 2.9
Time: 27.7s
Precision: 64
\[\left(-\left(df_sum \cdot dRho + \left(z2p \cdot \frac{1.0}{\sqrt{dist}} - \left(z2 \cdot \frac{1.0}{\sqrt{dist}}\right) \cdot \frac{1.0}{\sqrt{dist}}\right)\right)\right) \cdot \frac{1.0}{\sqrt{dist}}\]
\[\frac{\left(-\left(dRho \cdot df_sum + \left(z2p \cdot \frac{1.0}{\sqrt{dist}} - 1.0 \cdot \frac{z2}{dist}\right)\right)\right) \cdot 1.0}{\sqrt{dist}}\]
\left(-\left(df_sum \cdot dRho + \left(z2p \cdot \frac{1.0}{\sqrt{dist}} - \left(z2 \cdot \frac{1.0}{\sqrt{dist}}\right) \cdot \frac{1.0}{\sqrt{dist}}\right)\right)\right) \cdot \frac{1.0}{\sqrt{dist}}
\frac{\left(-\left(dRho \cdot df_sum + \left(z2p \cdot \frac{1.0}{\sqrt{dist}} - 1.0 \cdot \frac{z2}{dist}\right)\right)\right) \cdot 1.0}{\sqrt{dist}}
double f(double df_sum, double dRho, double z2p, double dist, double z2) {
        double r25776842 = df_sum;
        double r25776843 = dRho;
        double r25776844 = r25776842 * r25776843;
        double r25776845 = z2p;
        double r25776846 = 1.0;
        double r25776847 = dist;
        double r25776848 = sqrt(r25776847);
        double r25776849 = r25776846 / r25776848;
        double r25776850 = r25776845 * r25776849;
        double r25776851 = z2;
        double r25776852 = r25776851 * r25776849;
        double r25776853 = r25776852 * r25776849;
        double r25776854 = r25776850 - r25776853;
        double r25776855 = r25776844 + r25776854;
        double r25776856 = -r25776855;
        double r25776857 = r25776856 * r25776849;
        return r25776857;
}

double f(double df_sum, double dRho, double z2p, double dist, double z2) {
        double r25776858 = dRho;
        double r25776859 = df_sum;
        double r25776860 = r25776858 * r25776859;
        double r25776861 = z2p;
        double r25776862 = 1.0;
        double r25776863 = dist;
        double r25776864 = sqrt(r25776863);
        double r25776865 = r25776862 / r25776864;
        double r25776866 = r25776861 * r25776865;
        double r25776867 = z2;
        double r25776868 = r25776867 / r25776863;
        double r25776869 = r25776862 * r25776868;
        double r25776870 = r25776866 - r25776869;
        double r25776871 = r25776860 + r25776870;
        double r25776872 = -r25776871;
        double r25776873 = r25776872 * r25776862;
        double r25776874 = r25776873 / r25776864;
        return r25776874;
}

Error

Bits error versus df_sum

Bits error versus dRho

Bits error versus z2p

Bits error versus dist

Bits error versus z2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.1

    \[\left(-\left(df_sum \cdot dRho + \left(z2p \cdot \frac{1.0}{\sqrt{dist}} - \left(z2 \cdot \frac{1.0}{\sqrt{dist}}\right) \cdot \frac{1.0}{\sqrt{dist}}\right)\right)\right) \cdot \frac{1.0}{\sqrt{dist}}\]
  2. Taylor expanded around inf 3.0

    \[\leadsto \left(-\left(df_sum \cdot dRho + \left(z2p \cdot \frac{1.0}{\sqrt{dist}} - \color{blue}{1.0 \cdot \frac{z2}{dist}}\right)\right)\right) \cdot \frac{1.0}{\sqrt{dist}}\]
  3. Using strategy rm
  4. Applied associate-*r/2.9

    \[\leadsto \color{blue}{\frac{\left(-\left(df_sum \cdot dRho + \left(z2p \cdot \frac{1.0}{\sqrt{dist}} - 1.0 \cdot \frac{z2}{dist}\right)\right)\right) \cdot 1.0}{\sqrt{dist}}}\]
  5. Final simplification2.9

    \[\leadsto \frac{\left(-\left(dRho \cdot df_sum + \left(z2p \cdot \frac{1.0}{\sqrt{dist}} - 1.0 \cdot \frac{z2}{dist}\right)\right)\right) \cdot 1.0}{\sqrt{dist}}\]

Reproduce

herbie shell --seed 1 
(FPCore (df_sum dRho z2p dist z2)
  :name "-(df_sum * dRho + (z2p * (1.0 / (sqrt(dist)))- (z2 * (1.0 /(sqrt(dist))))* (1.0 / (sqrt(dist)))))* (1.0 / (sqrt(dist)))"
  (* (- (+ (* df_sum dRho) (- (* z2p (/ 1.0 (sqrt dist))) (* (* z2 (/ 1.0 (sqrt dist))) (/ 1.0 (sqrt dist)))))) (/ 1.0 (sqrt dist))))