3.9.2 imaginary part (p56)

Average Error: 0 → 0

Time: 22.9s

Precision: 64

Math

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

↓

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

C

double f() {
        double r1832219 = 1.0;
        double r1832220 = -r1832219;
        double r1832221 = 2.0;
        double r1832222 = r1832220 / r1832221;
        double r1832223 = 3.0;
        double r1832224 = sqrt(r1832223);
        double r1832225 = r1832224 / r1832221;
        double r1832226 = /* ERROR: no complex support in C */;
        double r1832227 = r1832226 * r1832226;
        double r1832228 = r1832227 * r1832226;
        double r1832229 = r1832228 * r1832226;
        double r1832230 = -r1832221;
        double r1832231 = 0.0;
        double r1832232 = /* ERROR: no complex support in C */;
        double r1832233 = r1832232 * r1832226;
        double r1832234 = r1832233 * r1832226;
        double r1832235 = r1832234 * r1832226;
        double r1832236 = r1832229 + r1832235;
        double r1832237 = 5.0;
        double r1832238 = /* ERROR: no complex support in C */;
        double r1832239 = r1832238 * r1832226;
        double r1832240 = r1832239 * r1832226;
        double r1832241 = r1832236 + r1832240;
        double r1832242 = 4.0;
        double r1832243 = /* ERROR: no complex support in C */;
        double r1832244 = r1832243 * r1832226;
        double r1832245 = r1832241 + r1832244;
        double r1832246 = 7.0;
        double r1832247 = /* ERROR: no complex support in C */;
        double r1832248 = r1832245 + r1832247;
        double r1832249 = /* ERROR: no complex support in C */;
        return r1832249;
}

↓

double f() {
        double r1832250 = 5.0;
        double r1832251 = 3.0;
        double r1832252 = sqrt(r1832251);
        double r1832253 = 2.0;
        double r1832254 = r1832252 / r1832253;
        double r1832255 = 4.0;
        double r1832256 = r1832254 * r1832255;
        double r1832257 = /* ERROR: no complex support in C */;
        double r1832258 = 6.0;
        double r1832259 = 0.25;
        double r1832260 = r1832254 * r1832254;
        double r1832261 = r1832259 - r1832260;
        double r1832262 = r1832258 + r1832261;
        double r1832263 = -r1832254;
        double r1832264 = -2.0;
        double r1832265 = r1832264 * r1832254;
        double r1832266 = r1832263 + r1832265;
        double r1832267 = /* ERROR: no complex support in C */;
        double r1832268 = /* ERROR: no complex support in C */;
        double r1832269 = r1832267 * r1832268;
        double r1832270 = r1832257 + r1832269;
        double r1832271 = /* ERROR: no complex support in C */;
        return r1832271;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019165 
(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))))