Average Error: 0.2 → 0.2
Time: 7.9s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\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(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 r144392 = a;
        double r144393 = r144392 * r144392;
        double r144394 = b;
        double r144395 = r144394 * r144394;
        double r144396 = r144393 + r144395;
        double r144397 = 2.0;
        double r144398 = pow(r144396, r144397);
        double r144399 = 4.0;
        double r144400 = 1.0;
        double r144401 = r144400 + r144392;
        double r144402 = r144393 * r144401;
        double r144403 = 3.0;
        double r144404 = r144403 * r144392;
        double r144405 = r144400 - r144404;
        double r144406 = r144395 * r144405;
        double r144407 = r144402 + r144406;
        double r144408 = r144399 * r144407;
        double r144409 = r144398 + r144408;
        double r144410 = r144409 - r144400;
        return r144410;
}
↓
double f(double a, double b) {
        double r144411 = a;
        double r144412 = r144411 * r144411;
        double r144413 = b;
        double r144414 = r144413 * r144413;
        double r144415 = r144412 + r144414;
        double r144416 = 2.0;
        double r144417 = pow(r144415, r144416);
        double r144418 = 4.0;
        double r144419 = 1.0;
        double r144420 = r144419 + r144411;
        double r144421 = r144412 * r144420;
        double r144422 = 3.0;
        double r144423 = r144422 * r144411;
        double r144424 = r144419 - r144423;
        double r144425 = r144414 * r144424;
        double r144426 = r144421 + r144425;
        double r144427 = r144418 * r144426;
        double r144428 = r144417 + r144427;
        double r144429 = r144428 - r144419;
        return r144429;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(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))