Average Error: 38.3 → 32.0
Time: 26.9s
Precision: 64
\[\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} + \frac{{s2}^{2}}{n2}}}\]
\[\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{\left(\frac{2}{2}\right)}}{\frac{n1}{{s1}^{\left(\frac{2}{2}\right)}}} + \frac{{s2}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{n2} \cdot \sqrt[3]{n2}} \cdot \frac{{s2}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{n2}}}}\]
\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} + \frac{{s2}^{2}}{n2}}}
\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{\left(\frac{2}{2}\right)}}{\frac{n1}{{s1}^{\left(\frac{2}{2}\right)}}} + \frac{{s2}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{n2} \cdot \sqrt[3]{n2}} \cdot \frac{{s2}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{n2}}}}
double f(double m1, double n1, double m2, double n2, double s1, double s2) {
        double r3402532 = m1;
        double r3402533 = n1;
        double r3402534 = r3402532 / r3402533;
        double r3402535 = m2;
        double r3402536 = n2;
        double r3402537 = r3402535 / r3402536;
        double r3402538 = r3402534 - r3402537;
        double r3402539 = s1;
        double r3402540 = 2.0;
        double r3402541 = pow(r3402539, r3402540);
        double r3402542 = r3402541 / r3402533;
        double r3402543 = s2;
        double r3402544 = pow(r3402543, r3402540);
        double r3402545 = r3402544 / r3402536;
        double r3402546 = r3402542 + r3402545;
        double r3402547 = sqrt(r3402546);
        double r3402548 = r3402538 / r3402547;
        return r3402548;
}

double f(double m1, double n1, double m2, double n2, double s1, double s2) {
        double r3402549 = m1;
        double r3402550 = n1;
        double r3402551 = r3402549 / r3402550;
        double r3402552 = m2;
        double r3402553 = n2;
        double r3402554 = r3402552 / r3402553;
        double r3402555 = r3402551 - r3402554;
        double r3402556 = s1;
        double r3402557 = 2.0;
        double r3402558 = 2.0;
        double r3402559 = r3402557 / r3402558;
        double r3402560 = pow(r3402556, r3402559);
        double r3402561 = r3402550 / r3402560;
        double r3402562 = r3402560 / r3402561;
        double r3402563 = s2;
        double r3402564 = pow(r3402563, r3402559);
        double r3402565 = cbrt(r3402553);
        double r3402566 = r3402565 * r3402565;
        double r3402567 = r3402564 / r3402566;
        double r3402568 = r3402564 / r3402565;
        double r3402569 = r3402567 * r3402568;
        double r3402570 = r3402562 + r3402569;
        double r3402571 = sqrt(r3402570);
        double r3402572 = r3402555 / r3402571;
        return r3402572;
}

Error

Bits error versus m1

Bits error versus n1

Bits error versus m2

Bits error versus n2

Bits error versus s1

Bits error versus s2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.3

    \[\frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{2}}{n1} + \frac{{s2}^{2}}{n2}}}\]
  2. Using strategy rm
  3. Applied sqr-pow38.3

    \[\leadsto \frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{\color{blue}{{s1}^{\left(\frac{2}{2}\right)} \cdot {s1}^{\left(\frac{2}{2}\right)}}}{n1} + \frac{{s2}^{2}}{n2}}}\]
  4. Applied associate-/l*35.2

    \[\leadsto \frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\color{blue}{\frac{{s1}^{\left(\frac{2}{2}\right)}}{\frac{n1}{{s1}^{\left(\frac{2}{2}\right)}}}} + \frac{{s2}^{2}}{n2}}}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt35.3

    \[\leadsto \frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{\left(\frac{2}{2}\right)}}{\frac{n1}{{s1}^{\left(\frac{2}{2}\right)}}} + \frac{{s2}^{2}}{\color{blue}{\left(\sqrt[3]{n2} \cdot \sqrt[3]{n2}\right) \cdot \sqrt[3]{n2}}}}}\]
  7. Applied sqr-pow35.3

    \[\leadsto \frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{\left(\frac{2}{2}\right)}}{\frac{n1}{{s1}^{\left(\frac{2}{2}\right)}}} + \frac{\color{blue}{{s2}^{\left(\frac{2}{2}\right)} \cdot {s2}^{\left(\frac{2}{2}\right)}}}{\left(\sqrt[3]{n2} \cdot \sqrt[3]{n2}\right) \cdot \sqrt[3]{n2}}}}\]
  8. Applied times-frac32.0

    \[\leadsto \frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{\left(\frac{2}{2}\right)}}{\frac{n1}{{s1}^{\left(\frac{2}{2}\right)}}} + \color{blue}{\frac{{s2}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{n2} \cdot \sqrt[3]{n2}} \cdot \frac{{s2}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{n2}}}}}\]
  9. Final simplification32.0

    \[\leadsto \frac{\frac{m1}{n1} - \frac{m2}{n2}}{\sqrt{\frac{{s1}^{\left(\frac{2}{2}\right)}}{\frac{n1}{{s1}^{\left(\frac{2}{2}\right)}}} + \frac{{s2}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{n2} \cdot \sqrt[3]{n2}} \cdot \frac{{s2}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{n2}}}}\]

Reproduce

herbie shell --seed 1 
(FPCore (m1 n1 m2 n2 s1 s2)
  :name "(m1/n1 - m2/n2) / sqrt( pow(s1, 2)/n1 + pow(s2, 2)/n2)"
  :precision binary64
  (/ (- (/ m1 n1) (/ m2 n2)) (sqrt (+ (/ (pow s1 2) n1) (/ (pow s2 2) n2)))))