3.9.2 imaginary part (p56)

Average Error: 0 → 0

Time: 31.9s

Precision: 64

Math

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

↓

\[\Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))\]

C

double f() {
        double r1412986 = 1.0;
        double r1412987 = -r1412986;
        double r1412988 = 2.0;
        double r1412989 = r1412987 / r1412988;
        double r1412990 = 3.0;
        double r1412991 = sqrt(r1412990);
        double r1412992 = r1412991 / r1412988;
        double r1412993 = /* ERROR: no complex support in C */;
        double r1412994 = r1412993 * r1412993;
        double r1412995 = r1412994 * r1412993;
        double r1412996 = r1412995 * r1412993;
        double r1412997 = -r1412988;
        double r1412998 = 0.0;
        double r1412999 = /* ERROR: no complex support in C */;
        double r1413000 = r1412999 * r1412993;
        double r1413001 = r1413000 * r1412993;
        double r1413002 = r1413001 * r1412993;
        double r1413003 = r1412996 + r1413002;
        double r1413004 = 5.0;
        double r1413005 = /* ERROR: no complex support in C */;
        double r1413006 = r1413005 * r1412993;
        double r1413007 = r1413006 * r1412993;
        double r1413008 = r1413003 + r1413007;
        double r1413009 = 4.0;
        double r1413010 = /* ERROR: no complex support in C */;
        double r1413011 = r1413010 * r1412993;
        double r1413012 = r1413008 + r1413011;
        double r1413013 = 7.0;
        double r1413014 = /* ERROR: no complex support in C */;
        double r1413015 = r1413012 + r1413014;
        double r1413016 = /* ERROR: no complex support in C */;
        return r1413016;
}

↓

double f() {
        double r1413017 = 5.0;
        double r1413018 = 3.0;
        double r1413019 = sqrt(r1413018);
        double r1413020 = 2.0;
        double r1413021 = r1413019 / r1413020;
        double r1413022 = 4.0;
        double r1413023 = r1413021 * r1413022;
        double r1413024 = /* ERROR: no complex support in C */;
        double r1413025 = 0.25;
        double r1413026 = r1413021 * r1413021;
        double r1413027 = r1413025 - r1413026;
        double r1413028 = -r1413019;
        double r1413029 = r1413028 / r1413020;
        double r1413030 = /* ERROR: no complex support in C */;
        double r1413031 = 6.0;
        double r1413032 = -2.0;
        double r1413033 = r1413032 * r1413019;
        double r1413034 = r1413033 / r1413020;
        double r1413035 = /* ERROR: no complex support in C */;
        double r1413036 = r1413035 + r1413030;
        double r1413037 = r1413030 * r1413036;
        double r1413038 = r1413024 + r1413037;
        double r1413039 = /* ERROR: no complex support in C */;
        return r1413039;
}

Derivation

1. Initial program 0

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

2. Simplified 0

   \[\leadsto \color{blue}{\Im(\left(\left(5 + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right) \cdot \left(\left(6 + \frac{\sqrt{3} \cdot -2}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right)\right)\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019124 +o rules:numerics
(FPCore ()
  :name "3.9.2 imaginary part (p56)"
  (im (+.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))))