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 r1329942 = 1.0;
        double r1329943 = -r1329942;
        double r1329944 = 2.0;
        double r1329945 = r1329943 / r1329944;
        double r1329946 = 3.0;
        double r1329947 = sqrt(r1329946);
        double r1329948 = r1329947 / r1329944;
        double r1329949 = /* ERROR: no complex support in C */;
        double r1329950 = r1329949 * r1329949;
        double r1329951 = r1329950 * r1329949;
        double r1329952 = r1329951 * r1329949;
        double r1329953 = -r1329944;
        double r1329954 = 0.0;
        double r1329955 = /* ERROR: no complex support in C */;
        double r1329956 = r1329955 * r1329949;
        double r1329957 = r1329956 * r1329949;
        double r1329958 = r1329957 * r1329949;
        double r1329959 = r1329952 + r1329958;
        double r1329960 = 5.0;
        double r1329961 = /* ERROR: no complex support in C */;
        double r1329962 = r1329961 * r1329949;
        double r1329963 = r1329962 * r1329949;
        double r1329964 = r1329959 + r1329963;
        double r1329965 = 4.0;
        double r1329966 = /* ERROR: no complex support in C */;
        double r1329967 = r1329966 * r1329949;
        double r1329968 = r1329964 + r1329967;
        double r1329969 = 7.0;
        double r1329970 = /* ERROR: no complex support in C */;
        double r1329971 = r1329968 + r1329970;
        double r1329972 = /* ERROR: no complex support in C */;
        return r1329972;
}

↓

double f() {
        double r1329973 = -5.0;
        double r1329974 = 3.0;
        double r1329975 = sqrt(r1329974);
        double r1329976 = -r1329975;
        double r1329977 = -4.0;
        double r1329978 = r1329976 / r1329977;
        double r1329979 = r1329978 + r1329978;
        double r1329980 = r1329975 / r1329977;
        double r1329981 = r1329980 + r1329980;
        double r1329982 = 10.0;
        double r1329983 = r1329982 * r1329980;
        double r1329984 = 2.0;
        double r1329985 = r1329975 / r1329984;
        double r1329986 = r1329983 + r1329985;
        double r1329987 = r1329981 + r1329986;
        double r1329988 = r1329979 + r1329987;
        double r1329989 = /* ERROR: no complex support in C */;
        double r1329990 = 5.0;
        double r1329991 = r1329975 * r1329984;
        double r1329992 = /* ERROR: no complex support in C */;
        double r1329993 = r1329989 + r1329992;
        double r1329994 = /* ERROR: no complex support in C */;
        return r1329994;
}

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 2019133 
(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))))