Average Error: 1.0 → 0
Time: 2.9s
Precision: 64
\[\frac{1}{10} + \frac{2}{10}\]
\[\frac{1}{\sqrt{10}} \cdot \left(\frac{1}{\sqrt{10}} + \frac{2}{\sqrt{10}}\right)\]
\frac{1}{10} + \frac{2}{10}
\frac{1}{\sqrt{10}} \cdot \left(\frac{1}{\sqrt{10}} + \frac{2}{\sqrt{10}}\right)
double f() {
        double r1865195 = 1.0;
        double r1865196 = 10.0;
        double r1865197 = r1865195 / r1865196;
        double r1865198 = 2.0;
        double r1865199 = r1865198 / r1865196;
        double r1865200 = r1865197 + r1865199;
        return r1865200;
}

double f() {
        double r1865201 = 1.0;
        double r1865202 = 10.0;
        double r1865203 = sqrt(r1865202);
        double r1865204 = r1865201 / r1865203;
        double r1865205 = 1.0;
        double r1865206 = r1865205 / r1865203;
        double r1865207 = 2.0;
        double r1865208 = r1865207 / r1865203;
        double r1865209 = r1865206 + r1865208;
        double r1865210 = r1865204 * r1865209;
        return r1865210;
}

Error

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    Results

    Enter valid numbers for all inputs

    Derivation

    1. Initial program 1.0

      \[\frac{1}{10} + \frac{2}{10}\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt1.0

      \[\leadsto \frac{1}{10} + \frac{2}{\color{blue}{\sqrt{10} \cdot \sqrt{10}}}\]
    4. Applied *-un-lft-identity1.0

      \[\leadsto \frac{1}{10} + \frac{\color{blue}{1 \cdot 2}}{\sqrt{10} \cdot \sqrt{10}}\]
    5. Applied times-frac1.0

      \[\leadsto \frac{1}{10} + \color{blue}{\frac{1}{\sqrt{10}} \cdot \frac{2}{\sqrt{10}}}\]
    6. Applied add-sqr-sqrt0

      \[\leadsto \frac{1}{\color{blue}{\sqrt{10} \cdot \sqrt{10}}} + \frac{1}{\sqrt{10}} \cdot \frac{2}{\sqrt{10}}\]
    7. Applied *-un-lft-identity0

      \[\leadsto \frac{\color{blue}{1 \cdot 1}}{\sqrt{10} \cdot \sqrt{10}} + \frac{1}{\sqrt{10}} \cdot \frac{2}{\sqrt{10}}\]
    8. Applied times-frac1.0

      \[\leadsto \color{blue}{\frac{1}{\sqrt{10}} \cdot \frac{1}{\sqrt{10}}} + \frac{1}{\sqrt{10}} \cdot \frac{2}{\sqrt{10}}\]
    9. Applied distribute-lft-out0

      \[\leadsto \color{blue}{\frac{1}{\sqrt{10}} \cdot \left(\frac{1}{\sqrt{10}} + \frac{2}{\sqrt{10}}\right)}\]
    10. Final simplification0

      \[\leadsto \frac{1}{\sqrt{10}} \cdot \left(\frac{1}{\sqrt{10}} + \frac{2}{\sqrt{10}}\right)\]

    Reproduce

    herbie shell --seed 1 
    (FPCore ()
      :name "1/10 + 2/10"
      :precision binary64
      (+ (/ 1 10) (/ 2 10)))