Average Error: 0.2 → 0.2
Time: 6.6s
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 r377284 = a;
        double r377285 = r377284 * r377284;
        double r377286 = b;
        double r377287 = r377286 * r377286;
        double r377288 = r377285 + r377287;
        double r377289 = 2.0;
        double r377290 = pow(r377288, r377289);
        double r377291 = 4.0;
        double r377292 = 1.0;
        double r377293 = r377292 + r377284;
        double r377294 = r377285 * r377293;
        double r377295 = 3.0;
        double r377296 = r377295 * r377284;
        double r377297 = r377292 - r377296;
        double r377298 = r377287 * r377297;
        double r377299 = r377294 + r377298;
        double r377300 = r377291 * r377299;
        double r377301 = r377290 + r377300;
        double r377302 = r377301 - r377292;
        return r377302;
}
↓
double f(double a, double b) {
        double r377303 = a;
        double r377304 = r377303 * r377303;
        double r377305 = b;
        double r377306 = r377305 * r377305;
        double r377307 = r377304 + r377306;
        double r377308 = 2.0;
        double r377309 = pow(r377307, r377308);
        double r377310 = 4.0;
        double r377311 = 1.0;
        double r377312 = r377311 + r377303;
        double r377313 = r377304 * r377312;
        double r377314 = 3.0;
        double r377315 = r377314 * r377303;
        double r377316 = r377311 - r377315;
        double r377317 = r377306 * r377316;
        double r377318 = r377313 + r377317;
        double r377319 = r377310 * r377318;
        double r377320 = r377309 + r377319;
        double r377321 = r377320 - r377311;
        return r377321;
}

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 2020021 +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))