quad2p (problem 3.2.1, positive)

Average Error: 1.7 → 1.7

Time: 22.9s

Precision: 64

Math

\[\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}\]

↓

\[\frac{\left(\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(c \cdot a\right)\right)}\right) - b_2\right)}{a}\]

C

double f(double a, double b_2, double c) {
        double r778946 = b_2;
        double r778947 = -r778946;
        double r778948 = r778946 * r778946;
        double r778949 = a;
        double r778950 = c;
        double r778951 = r778949 * r778950;
        double r778952 = r778948 - r778951;
        double r778953 = sqrt(r778952);
        double r778954 = r778947 + r778953;
        double r778955 = r778954 / r778949;
        return r778955;
}

↓

double f(double a, double b_2, double c) {
        double r778956 = b_2;
        double r778957 = r778956 * r778956;
        double r778958 = c;
        double r778959 = a;
        double r778960 = r778958 * r778959;
        double r778961 = r778957 - r778960;
        double r778962 = sqrt(r778961);
        double r778963 = r778962 - r778956;
        double r778964 = r778963 / r778959;
        return r778964;
}

Error

Bits error versus a

Bits error versus b_2

Bits error versus c

Derivation

1. Initial program 1.7

   \[\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}\]

2. Simplified 1.7

   \[\leadsto \color{blue}{\frac{\left(\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(c \cdot a\right)\right)}\right) - b_2\right)}{a}}\]

3. Final simplification 1.7

   \[\leadsto \frac{\left(\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(c \cdot a\right)\right)}\right) - b_2\right)}{a}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/.p16 (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a))