Average Error: 0.0 → 0.0
Time: 4.7s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[2 \cdot \frac{\frac{-\left(f + n\right)}{f - n}}{2}\]
\frac{-\left(f + n\right)}{f - n}
↓
2 \cdot \frac{\frac{-\left(f + n\right)}{f - n}}{2}
double f(double f, double n) {
        double r15450 = f;
        double r15451 = n;
        double r15452 = r15450 + r15451;
        double r15453 = -r15452;
        double r15454 = r15450 - r15451;
        double r15455 = r15453 / r15454;
        return r15455;
}
↓
double f(double f, double n) {
        double r15456 = 2.0;
        double r15457 = f;
        double r15458 = n;
        double r15459 = r15457 + r15458;
        double r15460 = -r15459;
        double r15461 = r15457 - r15458;
        double r15462 = r15460 / r15461;
        double r15463 = r15462 / r15456;
        double r15464 = r15456 * r15463;
        return r15464;
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.0

    \[\leadsto \log \color{blue}{\left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}} \cdot \sqrt{e^{\frac{-\left(f + n\right)}{f - n}}}\right)}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}} \cdot \sqrt{e^{\frac{-\left(f + n\right)}{\color{blue}{1 \cdot \left(f - n\right)}}}}\right)\]

  8. Applied *-un-lft-identity0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}} \cdot \sqrt{e^{\frac{\color{blue}{1 \cdot \left(-\left(f + n\right)\right)}}{1 \cdot \left(f - n\right)}}}\right)\]

  9. Applied times-frac0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}} \cdot \sqrt{e^{\color{blue}{\frac{1}{1} \cdot \frac{-\left(f + n\right)}{f - n}}}}\right)\]

  10. Applied exp-prod0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}} \cdot \sqrt{\color{blue}{{\left(e^{\frac{1}{1}}\right)}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}}}\right)\]

  11. Applied sqrt-pow10.0

    \[\leadsto \log \left(\sqrt{e^{\frac{-\left(f + n\right)}{f - n}}} \cdot \color{blue}{{\left(e^{\frac{1}{1}}\right)}^{\left(\frac{\frac{-\left(f + n\right)}{f - n}}{2}\right)}}\right)\]

  12. Applied *-un-lft-identity0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{-\left(f + n\right)}{\color{blue}{1 \cdot \left(f - n\right)}}}} \cdot {\left(e^{\frac{1}{1}}\right)}^{\left(\frac{\frac{-\left(f + n\right)}{f - n}}{2}\right)}\right)\]

  13. Applied *-un-lft-identity0.0

    \[\leadsto \log \left(\sqrt{e^{\frac{\color{blue}{1 \cdot \left(-\left(f + n\right)\right)}}{1 \cdot \left(f - n\right)}}} \cdot {\left(e^{\frac{1}{1}}\right)}^{\left(\frac{\frac{-\left(f + n\right)}{f - n}}{2}\right)}\right)\]

  14. Applied times-frac0.0

    \[\leadsto \log \left(\sqrt{e^{\color{blue}{\frac{1}{1} \cdot \frac{-\left(f + n\right)}{f - n}}}} \cdot {\left(e^{\frac{1}{1}}\right)}^{\left(\frac{\frac{-\left(f + n\right)}{f - n}}{2}\right)}\right)\]

  15. Applied exp-prod0.0

    \[\leadsto \log \left(\sqrt{\color{blue}{{\left(e^{\frac{1}{1}}\right)}^{\left(\frac{-\left(f + n\right)}{f - n}\right)}}} \cdot {\left(e^{\frac{1}{1}}\right)}^{\left(\frac{\frac{-\left(f + n\right)}{f - n}}{2}\right)}\right)\]

  16. Applied sqrt-pow10.0

    \[\leadsto \log \left(\color{blue}{{\left(e^{\frac{1}{1}}\right)}^{\left(\frac{\frac{-\left(f + n\right)}{f - n}}{2}\right)}} \cdot {\left(e^{\frac{1}{1}}\right)}^{\left(\frac{\frac{-\left(f + n\right)}{f - n}}{2}\right)}\right)\]

  17. Applied pow-sqr0.0

    \[\leadsto \log \color{blue}{\left({\left(e^{\frac{1}{1}}\right)}^{\left(2 \cdot \frac{\frac{-\left(f + n\right)}{f - n}}{2}\right)}\right)}\]

  18. Applied log-pow0.0

    \[\leadsto \color{blue}{\left(2 \cdot \frac{\frac{-\left(f + n\right)}{f - n}}{2}\right) \cdot \log \left(e^{\frac{1}{1}}\right)}\]

  19. Simplified0.0

    \[\leadsto \left(2 \cdot \frac{\frac{-\left(f + n\right)}{f - n}}{2}\right) \cdot \color{blue}{1}\]

  20. Final simplification0.0

    \[\leadsto 2 \cdot \frac{\frac{-\left(f + n\right)}{f - n}}{2}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))