Rosa's FloatVsDoubleBenchmark

Average Error: 0.5 → 0.5

Time: 1.4m

Precision: 64

Math

\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

↓

\[\left(\left(\left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1}, x1 \cdot x1 - 1, -3\right) + \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \mathsf{fma}\left(-3, 1, 3\right) + \left(0 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot -6\right) \cdot x1 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right)\right)\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right)\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) + x1\]

C

double f(double x1, double x2) {
        double r2934032 = x1;
        double r2934033 = 2.0;
        double r2934034 = r2934033 * r2934032;
        double r2934035 = 3.0;
        double r2934036 = r2934035 * r2934032;
        double r2934037 = r2934036 * r2934032;
        double r2934038 = x2;
        double r2934039 = r2934033 * r2934038;
        double r2934040 = r2934037 + r2934039;
        double r2934041 = r2934040 - r2934032;
        double r2934042 = r2934032 * r2934032;
        double r2934043 = 1.0;
        double r2934044 = r2934042 + r2934043;
        double r2934045 = r2934041 / r2934044;
        double r2934046 = r2934034 * r2934045;
        double r2934047 = r2934045 - r2934035;
        double r2934048 = r2934046 * r2934047;
        double r2934049 = 4.0;
        double r2934050 = r2934049 * r2934045;
        double r2934051 = 6.0;
        double r2934052 = r2934050 - r2934051;
        double r2934053 = r2934042 * r2934052;
        double r2934054 = r2934048 + r2934053;
        double r2934055 = r2934054 * r2934044;
        double r2934056 = r2934037 * r2934045;
        double r2934057 = r2934055 + r2934056;
        double r2934058 = r2934042 * r2934032;
        double r2934059 = r2934057 + r2934058;
        double r2934060 = r2934059 + r2934032;
        double r2934061 = r2934037 - r2934039;
        double r2934062 = r2934061 - r2934032;
        double r2934063 = r2934062 / r2934044;
        double r2934064 = r2934035 * r2934063;
        double r2934065 = r2934060 + r2934064;
        double r2934066 = r2934032 + r2934065;
        return r2934066;
}

↓

double f(double x1, double x2) {
        double r2934067 = x1;
        double r2934068 = r2934067 * r2934067;
        double r2934069 = r2934067 * r2934068;
        double r2934070 = 1.0;
        double r2934071 = r2934070 + r2934068;
        double r2934072 = 2.0;
        double r2934073 = r2934067 * r2934072;
        double r2934074 = 3.0;
        double r2934075 = r2934074 * r2934067;
        double r2934076 = r2934075 * r2934067;
        double r2934077 = x2;
        double r2934078 = r2934077 * r2934072;
        double r2934079 = r2934076 + r2934078;
        double r2934080 = r2934079 - r2934067;
        double r2934081 = r2934080 / r2934071;
        double r2934082 = r2934073 * r2934081;
        double r2934083 = r2934068 * r2934068;
        double r2934084 = r2934083 - r2934070;
        double r2934085 = r2934080 / r2934084;
        double r2934086 = r2934068 - r2934070;
        double r2934087 = -3.0;
        double r2934088 = fma(r2934085, r2934086, r2934087);
        double r2934089 = r2934082 * r2934088;
        double r2934090 = fma(r2934087, r2934070, r2934074);
        double r2934091 = r2934082 * r2934090;
        double r2934092 = 0.0;
        double r2934093 = r2934092 * r2934068;
        double r2934094 = -6.0;
        double r2934095 = r2934067 * r2934094;
        double r2934096 = r2934095 * r2934067;
        double r2934097 = 4.0;
        double r2934098 = r2934097 * r2934081;
        double r2934099 = r2934068 * r2934098;
        double r2934100 = r2934096 + r2934099;
        double r2934101 = r2934093 + r2934100;
        double r2934102 = r2934091 + r2934101;
        double r2934103 = r2934089 + r2934102;
        double r2934104 = r2934071 * r2934103;
        double r2934105 = r2934076 * r2934081;
        double r2934106 = r2934104 + r2934105;
        double r2934107 = r2934069 + r2934106;
        double r2934108 = r2934107 + r2934067;
        double r2934109 = r2934076 - r2934078;
        double r2934110 = r2934109 - r2934067;
        double r2934111 = r2934110 / r2934071;
        double r2934112 = r2934074 * r2934111;
        double r2934113 = r2934108 + r2934112;
        double r2934114 = r2934113 + r2934067;
        return r2934114;
}

Error

Bits error versus x1

Bits error versus x2

Derivation

1. Initial program 0.5

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
2. Using strategy rm

3. Applied *-un-lft-identity 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \color{blue}{1 \cdot 3}\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

4. Applied flip-+ 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\color{blue}{\frac{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}{x1 \cdot x1 - 1}}} - 1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

5. Applied associate-/r/ 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\color{blue}{\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1} \cdot \left(x1 \cdot x1 - 1\right)} - 1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

6. Applied prod-diff 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \color{blue}{\left(\mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \mathsf{fma}\left(-3, 1, 3 \cdot 1\right)\right)} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

7. Applied distribute-lft-in 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right)\right)} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

8. Applied associate-+l+ 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
9. Using strategy rm

10. Applied add-sqr-sqrt 0.6

    \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \color{blue}{\sqrt{6} \cdot \sqrt{6}}\right)\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

11. Applied prod-diff 0.6

    \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right) + \left(x1 \cdot x1\right) \cdot \color{blue}{\left(\mathsf{fma}\left(4, \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}, -\sqrt{6} \cdot \sqrt{6}\right) + \mathsf{fma}\left(-\sqrt{6}, \sqrt{6}, \sqrt{6} \cdot \sqrt{6}\right)\right)}\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

12. Applied distribute-lft-in 0.6

    \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right) + \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}, -\sqrt{6} \cdot \sqrt{6}\right) + \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(-\sqrt{6}, \sqrt{6}, \sqrt{6} \cdot \sqrt{6}\right)\right)}\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

13. Simplified 0.6

    \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right) + \left(\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}, -\sqrt{6} \cdot \sqrt{6}\right) + \color{blue}{0 \cdot \left(x1 \cdot x1\right)}\right)\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
14. Using strategy rm

15. Applied fma-udef 0.6

    \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right) + \left(\left(x1 \cdot x1\right) \cdot \color{blue}{\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(-\sqrt{6} \cdot \sqrt{6}\right)\right)} + 0 \cdot \left(x1 \cdot x1\right)\right)\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

16. Applied distribute-rgt-in 0.5

    \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right) + \left(\color{blue}{\left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(x1 \cdot x1\right) + \left(-\sqrt{6} \cdot \sqrt{6}\right) \cdot \left(x1 \cdot x1\right)\right)} + 0 \cdot \left(x1 \cdot x1\right)\right)\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

17. Simplified 0.5

    \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1 \cdot 1}, x1 \cdot x1 - 1, -3 \cdot 1\right) + \left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \mathsf{fma}\left(-3, 1, 3 \cdot 1\right) + \left(\left(\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(x1 \cdot x1\right) + \color{blue}{\left(x1 \cdot -6\right) \cdot x1}\right) + 0 \cdot \left(x1 \cdot x1\right)\right)\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

18. Final simplification 0.5

    \[\leadsto \left(\left(\left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \mathsf{fma}\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right) - 1}, x1 \cdot x1 - 1, -3\right) + \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) \cdot \mathsf{fma}\left(-3, 1, 3\right) + \left(0 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot -6\right) \cdot x1 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right)\right)\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right)\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right) + x1\]

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1)) x1) (* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))))))