3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 30.5s

Precision: 64

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

↓

\[\Re(\left(\left(-5 + \left(\left(\frac{-\sqrt{3}}{-4} + \frac{-\sqrt{3}}{-4}\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(10 \cdot \frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{2}\right)\right)\right) i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

C

double f() {
        double r1319942 = 1.0;
        double r1319943 = -r1319942;
        double r1319944 = 2.0;
        double r1319945 = r1319943 / r1319944;
        double r1319946 = 3.0;
        double r1319947 = sqrt(r1319946);
        double r1319948 = r1319947 / r1319944;
        double r1319949 = /* ERROR: no complex support in C */;
        double r1319950 = r1319949 * r1319949;
        double r1319951 = r1319950 * r1319949;
        double r1319952 = r1319951 * r1319949;
        double r1319953 = -r1319944;
        double r1319954 = 0.0;
        double r1319955 = /* ERROR: no complex support in C */;
        double r1319956 = r1319955 * r1319949;
        double r1319957 = r1319956 * r1319949;
        double r1319958 = r1319957 * r1319949;
        double r1319959 = r1319952 + r1319958;
        double r1319960 = 5.0;
        double r1319961 = /* ERROR: no complex support in C */;
        double r1319962 = r1319961 * r1319949;
        double r1319963 = r1319962 * r1319949;
        double r1319964 = r1319959 + r1319963;
        double r1319965 = 4.0;
        double r1319966 = /* ERROR: no complex support in C */;
        double r1319967 = r1319966 * r1319949;
        double r1319968 = r1319964 + r1319967;
        double r1319969 = 7.0;
        double r1319970 = /* ERROR: no complex support in C */;
        double r1319971 = r1319968 + r1319970;
        double r1319972 = /* ERROR: no complex support in C */;
        return r1319972;
}

↓

double f() {
        double r1319973 = -5.0;
        double r1319974 = 3.0;
        double r1319975 = sqrt(r1319974);
        double r1319976 = -r1319975;
        double r1319977 = -4.0;
        double r1319978 = r1319976 / r1319977;
        double r1319979 = r1319978 + r1319978;
        double r1319980 = r1319975 / r1319977;
        double r1319981 = r1319980 + r1319980;
        double r1319982 = 10.0;
        double r1319983 = r1319982 * r1319980;
        double r1319984 = 2.0;
        double r1319985 = r1319975 / r1319984;
        double r1319986 = r1319983 + r1319985;
        double r1319987 = r1319981 + r1319986;
        double r1319988 = r1319979 + r1319987;
        double r1319989 = /* ERROR: no complex support in C */;
        double r1319990 = 5.0;
        double r1319991 = r1319975 * r1319984;
        double r1319992 = /* ERROR: no complex support in C */;
        double r1319993 = r1319989 + r1319992;
        double r1319994 = /* ERROR: no complex support in C */;
        return r1319994;
}

Derivation

1. Initial program 61.9

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Re(\left(\left(5 + 2 \cdot \sqrt{3} i\right) + \left(-5 + \left(\left(\left(-\frac{\sqrt{3}}{-4}\right) + \left(-\frac{\sqrt{3}}{-4}\right)\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{-4} \cdot 10\right)\right)\right) i\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(-5 + \left(\left(\frac{-\sqrt{3}}{-4} + \frac{-\sqrt{3}}{-4}\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(10 \cdot \frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{2}\right)\right)\right) i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

Reproduce

herbie shell --seed 2019130 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+.c (+.c (+.c (+.c (*.c (*.c (*.c (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (*.c (*.c (*.c (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (*.c (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))