Average Error: 0.2 → 0.2
Time: 30.1s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\sqrt{{\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4} \cdot \sqrt{{\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4} - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\sqrt{{\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4} \cdot \sqrt{{\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a + 3\right) \cdot \left(b \cdot b\right) + \left(a \cdot a\right) \cdot \left(1 - a\right)\right) \cdot 4} - 1
double f(double a, double b) {
        double r103232555 = a;
        double r103232556 = r103232555 * r103232555;
        double r103232557 = b;
        double r103232558 = r103232557 * r103232557;
        double r103232559 = r103232556 + r103232558;
        double r103232560 = 2.0;
        double r103232561 = pow(r103232559, r103232560);
        double r103232562 = 4.0;
        double r103232563 = 1.0;
        double r103232564 = r103232563 - r103232555;
        double r103232565 = r103232556 * r103232564;
        double r103232566 = 3.0;
        double r103232567 = r103232566 + r103232555;
        double r103232568 = r103232558 * r103232567;
        double r103232569 = r103232565 + r103232568;
        double r103232570 = r103232562 * r103232569;
        double r103232571 = r103232561 + r103232570;
        double r103232572 = r103232571 - r103232563;
        return r103232572;
}
↓
double f(double a, double b) {
        double r103232573 = a;
        double r103232574 = r103232573 * r103232573;
        double r103232575 = b;
        double r103232576 = r103232575 * r103232575;
        double r103232577 = r103232574 + r103232576;
        double r103232578 = 2.0;
        double r103232579 = pow(r103232577, r103232578);
        double r103232580 = 3.0;
        double r103232581 = r103232573 + r103232580;
        double r103232582 = r103232581 * r103232576;
        double r103232583 = 1.0;
        double r103232584 = r103232583 - r103232573;
        double r103232585 = r103232574 * r103232584;
        double r103232586 = r103232582 + r103232585;
        double r103232587 = 4.0;
        double r103232588 = r103232586 * r103232587;
        double r103232589 = r103232579 + r103232588;
        double r103232590 = sqrt(r103232589);
        double r103232591 = r103232590 * r103232590;
        double r103232592 = r103232591 - r103232583;
        return r103232592;
}

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

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

  3. Applied add-sqr-sqrt0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019107 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))