Average Error: 0.5 → 0.5
Time: 58.2s
Precision: 64
\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
↓
\[\left(\frac{\left(x1 \cdot x1\right) \cdot 3 - \left(x1 - -2 \cdot x2\right)}{1 + x1 \cdot x1} \cdot 3 + x1\right) + \left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(2 \cdot x2 - x1\right)}{1 + x1 \cdot x1} \cdot \left(\left(x1 \cdot x1\right) \cdot 3 + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(2 \cdot x2 - x1\right)}{1 + x1 \cdot x1} - 3\right)\right) \cdot \left(2 \cdot x1\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(-6 \cdot \left(x1 \cdot x1\right) + \left(x1 \cdot \frac{4 \cdot \left(\left(x1 \cdot x1\right) \cdot 3 + \left(2 \cdot x2 - x1\right)\right)}{1 + x1 \cdot x1}\right) \cdot x1\right) + x1\right)\right)\]
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(\frac{\left(x1 \cdot x1\right) \cdot 3 - \left(x1 - -2 \cdot x2\right)}{1 + x1 \cdot x1} \cdot 3 + x1\right) + \left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(2 \cdot x2 - x1\right)}{1 + x1 \cdot x1} \cdot \left(\left(x1 \cdot x1\right) \cdot 3 + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(2 \cdot x2 - x1\right)}{1 + x1 \cdot x1} - 3\right)\right) \cdot \left(2 \cdot x1\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(-6 \cdot \left(x1 \cdot x1\right) + \left(x1 \cdot \frac{4 \cdot \left(\left(x1 \cdot x1\right) \cdot 3 + \left(2 \cdot x2 - x1\right)\right)}{1 + x1 \cdot x1}\right) \cdot x1\right) + x1\right)\right)
double f(double x1, double x2) {
        double r2916138 = x1;
        double r2916139 = 2.0;
        double r2916140 = r2916139 * r2916138;
        double r2916141 = 3.0;
        double r2916142 = r2916141 * r2916138;
        double r2916143 = r2916142 * r2916138;
        double r2916144 = x2;
        double r2916145 = r2916139 * r2916144;
        double r2916146 = r2916143 + r2916145;
        double r2916147 = r2916146 - r2916138;
        double r2916148 = r2916138 * r2916138;
        double r2916149 = 1.0;
        double r2916150 = r2916148 + r2916149;
        double r2916151 = r2916147 / r2916150;
        double r2916152 = r2916140 * r2916151;
        double r2916153 = r2916151 - r2916141;
        double r2916154 = r2916152 * r2916153;
        double r2916155 = 4.0;
        double r2916156 = r2916155 * r2916151;
        double r2916157 = 6.0;
        double r2916158 = r2916156 - r2916157;
        double r2916159 = r2916148 * r2916158;
        double r2916160 = r2916154 + r2916159;
        double r2916161 = r2916160 * r2916150;
        double r2916162 = r2916143 * r2916151;
        double r2916163 = r2916161 + r2916162;
        double r2916164 = r2916148 * r2916138;
        double r2916165 = r2916163 + r2916164;
        double r2916166 = r2916165 + r2916138;
        double r2916167 = r2916143 - r2916145;
        double r2916168 = r2916167 - r2916138;
        double r2916169 = r2916168 / r2916150;
        double r2916170 = r2916141 * r2916169;
        double r2916171 = r2916166 + r2916170;
        double r2916172 = r2916138 + r2916171;
        return r2916172;
}
↓
double f(double x1, double x2) {
        double r2916173 = x1;
        double r2916174 = r2916173 * r2916173;
        double r2916175 = 3.0;
        double r2916176 = r2916174 * r2916175;
        double r2916177 = -2.0;
        double r2916178 = x2;
        double r2916179 = r2916177 * r2916178;
        double r2916180 = r2916173 - r2916179;
        double r2916181 = r2916176 - r2916180;
        double r2916182 = 1.0;
        double r2916183 = r2916182 + r2916174;
        double r2916184 = r2916181 / r2916183;
        double r2916185 = r2916184 * r2916175;
        double r2916186 = r2916185 + r2916173;
        double r2916187 = 2.0;
        double r2916188 = r2916187 * r2916178;
        double r2916189 = r2916188 - r2916173;
        double r2916190 = r2916176 + r2916189;
        double r2916191 = r2916190 / r2916183;
        double r2916192 = r2916191 - r2916175;
        double r2916193 = r2916183 * r2916192;
        double r2916194 = r2916187 * r2916173;
        double r2916195 = r2916193 * r2916194;
        double r2916196 = r2916176 + r2916195;
        double r2916197 = r2916191 * r2916196;
        double r2916198 = -6.0;
        double r2916199 = r2916198 * r2916174;
        double r2916200 = 4.0;
        double r2916201 = r2916200 * r2916190;
        double r2916202 = r2916201 / r2916183;
        double r2916203 = r2916173 * r2916202;
        double r2916204 = r2916203 * r2916173;
        double r2916205 = r2916199 + r2916204;
        double r2916206 = r2916205 + r2916173;
        double r2916207 = r2916183 * r2916206;
        double r2916208 = r2916197 + r2916207;
        double r2916209 = r2916186 + r2916208;
        return r2916209;
}

Error

Bits error versus x1

Bits error versus x2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified0.5

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

  4. Applied distribute-rgt-in0.5

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

  6. Applied associate-*r*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019132 
(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))))))