Average Error: 0.2 → 0.7
Time: 16.4s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(\sqrt[3]{a \cdot a + b \cdot b} \cdot \sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left({\left(\sqrt[3]{a \cdot a + b \cdot b} \cdot \sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
double f(double a, double b) {
        double r144035 = a;
        double r144036 = r144035 * r144035;
        double r144037 = b;
        double r144038 = r144037 * r144037;
        double r144039 = r144036 + r144038;
        double r144040 = 2.0;
        double r144041 = pow(r144039, r144040);
        double r144042 = 4.0;
        double r144043 = 1.0;
        double r144044 = r144043 + r144035;
        double r144045 = r144036 * r144044;
        double r144046 = 3.0;
        double r144047 = r144046 * r144035;
        double r144048 = r144043 - r144047;
        double r144049 = r144038 * r144048;
        double r144050 = r144045 + r144049;
        double r144051 = r144042 * r144050;
        double r144052 = r144041 + r144051;
        double r144053 = r144052 - r144043;
        return r144053;
}
↓
double f(double a, double b) {
        double r144054 = a;
        double r144055 = r144054 * r144054;
        double r144056 = b;
        double r144057 = r144056 * r144056;
        double r144058 = r144055 + r144057;
        double r144059 = cbrt(r144058);
        double r144060 = r144059 * r144059;
        double r144061 = 2.0;
        double r144062 = pow(r144060, r144061);
        double r144063 = pow(r144059, r144061);
        double r144064 = r144062 * r144063;
        double r144065 = 4.0;
        double r144066 = 1.0;
        double r144067 = r144066 + r144054;
        double r144068 = r144055 * r144067;
        double r144069 = 3.0;
        double r144070 = r144069 * r144054;
        double r144071 = r144066 - r144070;
        double r144072 = r144057 * r144071;
        double r144073 = r144068 + r144072;
        double r144074 = r144065 * r144073;
        double r144075 = r144064 + r144074;
        double r144076 = r144075 - r144066;
        return r144076;
}

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

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.7

    \[\leadsto \left({\color{blue}{\left(\left(\sqrt[3]{a \cdot a + b \cdot b} \cdot \sqrt[3]{a \cdot a + b \cdot b}\right) \cdot \sqrt[3]{a \cdot a + b \cdot b}\right)}}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

  4. Applied unpow-prod-down0.7

    \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{a \cdot a + b \cdot b} \cdot \sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2}} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

  5. Final simplification0.7

    \[\leadsto \left({\left(\sqrt[3]{a \cdot a + b \cdot b} \cdot \sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

Reproduce

herbie shell --seed 2019303 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))