Average Error: 0.6 → 0.3
Time: 29.4s
Precision: 64
\[4 \le x1 \le 6.360000000000000319744231092045083642006 \land 4 \le x2 \le 6.360000000000000319744231092045083642006 \land 4 \le x3 \le 6.360000000000000319744231092045083642006 \land 4 \le x4 \le 6.360000000000000319744231092045083642006 \land 4 \le x5 \le 6.360000000000000319744231092045083642006 \land 4 \le x6 \le 6.360000000000000319744231092045083642006\]
\[\left(\left(\left(x2 \cdot x5 + x3 \cdot x6\right) - x2 \cdot x3\right) - x5 \cdot x6\right) + x1 \cdot \left(\left(\left(\left(\left(\left(-x1\right) + x2\right) + x3\right) - x4\right) + x5\right) + x6\right)\]
\[\left(\left(\left(-x5\right) \cdot x6 + \left(x2 \cdot x5 + \left(x6 - x2\right) \cdot x3\right)\right) + \left(x6 + \left(\left(\left(x2 - x1\right) + x3\right) - x4\right)\right) \cdot x1\right) + x1 \cdot x5\]
\left(\left(\left(x2 \cdot x5 + x3 \cdot x6\right) - x2 \cdot x3\right) - x5 \cdot x6\right) + x1 \cdot \left(\left(\left(\left(\left(\left(-x1\right) + x2\right) + x3\right) - x4\right) + x5\right) + x6\right)
\left(\left(\left(-x5\right) \cdot x6 + \left(x2 \cdot x5 + \left(x6 - x2\right) \cdot x3\right)\right) + \left(x6 + \left(\left(\left(x2 - x1\right) + x3\right) - x4\right)\right) \cdot x1\right) + x1 \cdot x5
double f(double x1, double x2, double x3, double x4, double x5, double x6) {
        double r2839091 = x2;
        double r2839092 = x5;
        double r2839093 = r2839091 * r2839092;
        double r2839094 = x3;
        double r2839095 = x6;
        double r2839096 = r2839094 * r2839095;
        double r2839097 = r2839093 + r2839096;
        double r2839098 = r2839091 * r2839094;
        double r2839099 = r2839097 - r2839098;
        double r2839100 = r2839092 * r2839095;
        double r2839101 = r2839099 - r2839100;
        double r2839102 = x1;
        double r2839103 = -r2839102;
        double r2839104 = r2839103 + r2839091;
        double r2839105 = r2839104 + r2839094;
        double r2839106 = x4;
        double r2839107 = r2839105 - r2839106;
        double r2839108 = r2839107 + r2839092;
        double r2839109 = r2839108 + r2839095;
        double r2839110 = r2839102 * r2839109;
        double r2839111 = r2839101 + r2839110;
        return r2839111;
}

double f(double x1, double x2, double x3, double x4, double x5, double x6) {
        double r2839112 = x5;
        double r2839113 = -r2839112;
        double r2839114 = x6;
        double r2839115 = r2839113 * r2839114;
        double r2839116 = x2;
        double r2839117 = r2839116 * r2839112;
        double r2839118 = r2839114 - r2839116;
        double r2839119 = x3;
        double r2839120 = r2839118 * r2839119;
        double r2839121 = r2839117 + r2839120;
        double r2839122 = r2839115 + r2839121;
        double r2839123 = x1;
        double r2839124 = r2839116 - r2839123;
        double r2839125 = r2839124 + r2839119;
        double r2839126 = x4;
        double r2839127 = r2839125 - r2839126;
        double r2839128 = r2839114 + r2839127;
        double r2839129 = r2839128 * r2839123;
        double r2839130 = r2839122 + r2839129;
        double r2839131 = r2839123 * r2839112;
        double r2839132 = r2839130 + r2839131;
        return r2839132;
}

Error

Bits error versus x1

Bits error versus x2

Bits error versus x3

Bits error versus x4

Bits error versus x5

Bits error versus x6

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[\left(\left(\left(x2 \cdot x5 + x3 \cdot x6\right) - x2 \cdot x3\right) - x5 \cdot x6\right) + x1 \cdot \left(\left(\left(\left(\left(\left(-x1\right) + x2\right) + x3\right) - x4\right) + x5\right) + x6\right)\]
  2. Simplified0.4

    \[\leadsto \color{blue}{x1 \cdot \left(x5 + \left(x6 + \left(\left(x3 + \left(x2 - x1\right)\right) - x4\right)\right)\right) + \left(\left(x6 - x2\right) \cdot x3 + x5 \cdot \left(x2 - x6\right)\right)}\]
  3. Using strategy rm
  4. Applied distribute-rgt-in0.3

    \[\leadsto \color{blue}{\left(x5 \cdot x1 + \left(x6 + \left(\left(x3 + \left(x2 - x1\right)\right) - x4\right)\right) \cdot x1\right)} + \left(\left(x6 - x2\right) \cdot x3 + x5 \cdot \left(x2 - x6\right)\right)\]
  5. Applied associate-+l+0.3

    \[\leadsto \color{blue}{x5 \cdot x1 + \left(\left(x6 + \left(\left(x3 + \left(x2 - x1\right)\right) - x4\right)\right) \cdot x1 + \left(\left(x6 - x2\right) \cdot x3 + x5 \cdot \left(x2 - x6\right)\right)\right)}\]
  6. Using strategy rm
  7. Applied sub-neg0.3

    \[\leadsto x5 \cdot x1 + \left(\left(x6 + \left(\left(x3 + \left(x2 - x1\right)\right) - x4\right)\right) \cdot x1 + \left(\left(x6 - x2\right) \cdot x3 + x5 \cdot \color{blue}{\left(x2 + \left(-x6\right)\right)}\right)\right)\]
  8. Applied distribute-lft-in0.3

    \[\leadsto x5 \cdot x1 + \left(\left(x6 + \left(\left(x3 + \left(x2 - x1\right)\right) - x4\right)\right) \cdot x1 + \left(\left(x6 - x2\right) \cdot x3 + \color{blue}{\left(x5 \cdot x2 + x5 \cdot \left(-x6\right)\right)}\right)\right)\]
  9. Applied associate-+r+0.3

    \[\leadsto x5 \cdot x1 + \left(\left(x6 + \left(\left(x3 + \left(x2 - x1\right)\right) - x4\right)\right) \cdot x1 + \color{blue}{\left(\left(\left(x6 - x2\right) \cdot x3 + x5 \cdot x2\right) + x5 \cdot \left(-x6\right)\right)}\right)\]
  10. Final simplification0.3

    \[\leadsto \left(\left(\left(-x5\right) \cdot x6 + \left(x2 \cdot x5 + \left(x6 - x2\right) \cdot x3\right)\right) + \left(x6 + \left(\left(\left(x2 - x1\right) + x3\right) - x4\right)\right) \cdot x1\right) + x1 \cdot x5\]

Reproduce

herbie shell --seed 1 
(FPCore (x1 x2 x3 x4 x5 x6)
  :name "kepler0"
  :pre (and (<= 4.0 x1 6.36) (<= 4.0 x2 6.36) (<= 4.0 x3 6.36) (<= 4.0 x4 6.36) (<= 4.0 x5 6.36) (<= 4.0 x6 6.36))
  (+ (- (- (+ (* x2 x5) (* x3 x6)) (* x2 x3)) (* x5 x6)) (* x1 (+ (+ (- (+ (+ (- x1) x2) x3) x4) x5) x6))))