Average Error: 0.2 → 0.2
Time: 17.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left(\left(\sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4}\right) \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\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]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4}\right) \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r5695018 = a;
        double r5695019 = r5695018 * r5695018;
        double r5695020 = b;
        double r5695021 = r5695020 * r5695020;
        double r5695022 = r5695019 + r5695021;
        double r5695023 = 2.0;
        double r5695024 = pow(r5695022, r5695023);
        double r5695025 = 4.0;
        double r5695026 = 1.0;
        double r5695027 = r5695026 + r5695018;
        double r5695028 = r5695019 * r5695027;
        double r5695029 = 3.0;
        double r5695030 = r5695029 * r5695018;
        double r5695031 = r5695026 - r5695030;
        double r5695032 = r5695021 * r5695031;
        double r5695033 = r5695028 + r5695032;
        double r5695034 = r5695025 * r5695033;
        double r5695035 = r5695024 + r5695034;
        double r5695036 = r5695035 - r5695026;
        return r5695036;
}
↓
double f(double a, double b) {
        double r5695037 = a;
        double r5695038 = r5695037 * r5695037;
        double r5695039 = 1.0;
        double r5695040 = r5695037 + r5695039;
        double r5695041 = r5695038 * r5695040;
        double r5695042 = b;
        double r5695043 = r5695042 * r5695042;
        double r5695044 = 3.0;
        double r5695045 = r5695044 * r5695037;
        double r5695046 = r5695039 - r5695045;
        double r5695047 = r5695043 * r5695046;
        double r5695048 = r5695041 + r5695047;
        double r5695049 = 4.0;
        double r5695050 = r5695048 * r5695049;
        double r5695051 = cbrt(r5695050);
        double r5695052 = r5695051 * r5695051;
        double r5695053 = r5695052 * r5695051;
        double r5695054 = r5695038 + r5695043;
        double r5695055 = 2.0;
        double r5695056 = pow(r5695054, r5695055);
        double r5695057 = r5695053 + r5695056;
        double r5695058 = r5695057 - r5695039;
        return r5695058;
}

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-cbrt0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))