Average Error: 0.2 → 0.2
Time: 12.9s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
double f(double a, double b) {
        double r108093 = a;
        double r108094 = r108093 * r108093;
        double r108095 = b;
        double r108096 = r108095 * r108095;
        double r108097 = r108094 + r108096;
        double r108098 = 2.0;
        double r108099 = pow(r108097, r108098);
        double r108100 = 4.0;
        double r108101 = r108100 * r108096;
        double r108102 = r108099 + r108101;
        double r108103 = 1.0;
        double r108104 = r108102 - r108103;
        return r108104;
}
↓
double f(double a, double b) {
        double r108105 = a;
        double r108106 = r108105 * r108105;
        double r108107 = b;
        double r108108 = r108107 * r108107;
        double r108109 = r108106 + r108108;
        double r108110 = 2.0;
        double r108111 = pow(r108109, r108110);
        double r108112 = 4.0;
        double r108113 = r108112 * r108108;
        double r108114 = r108111 + r108113;
        double r108115 = 1.0;
        double r108116 = r108114 - r108115;
        return r108116;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

  2. Final simplification0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

Reproduce

herbie shell --seed 2019291 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))