3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 30.7s

Precision: 64

Math

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

↓

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

C

double f() {
        double r2324315 = 1.0;
        double r2324316 = -r2324315;
        double r2324317 = 2.0;
        double r2324318 = r2324316 / r2324317;
        double r2324319 = 3.0;
        double r2324320 = sqrt(r2324319);
        double r2324321 = r2324320 / r2324317;
        double r2324322 = /* ERROR: no complex support in C */;
        double r2324323 = r2324322 * r2324322;
        double r2324324 = r2324323 * r2324322;
        double r2324325 = r2324324 * r2324322;
        double r2324326 = -r2324317;
        double r2324327 = 0.0;
        double r2324328 = /* ERROR: no complex support in C */;
        double r2324329 = r2324328 * r2324322;
        double r2324330 = r2324329 * r2324322;
        double r2324331 = r2324330 * r2324322;
        double r2324332 = r2324325 + r2324331;
        double r2324333 = 5.0;
        double r2324334 = /* ERROR: no complex support in C */;
        double r2324335 = r2324334 * r2324322;
        double r2324336 = r2324335 * r2324322;
        double r2324337 = r2324332 + r2324336;
        double r2324338 = 4.0;
        double r2324339 = /* ERROR: no complex support in C */;
        double r2324340 = r2324339 * r2324322;
        double r2324341 = r2324337 + r2324340;
        double r2324342 = 7.0;
        double r2324343 = /* ERROR: no complex support in C */;
        double r2324344 = r2324341 + r2324343;
        double r2324345 = /* ERROR: no complex support in C */;
        return r2324345;
}

↓

double f() {
        double r2324346 = 5.0;
        double r2324347 = 3.0;
        double r2324348 = sqrt(r2324347);
        double r2324349 = 2.0;
        double r2324350 = r2324348 / r2324349;
        double r2324351 = 4.0;
        double r2324352 = r2324350 * r2324351;
        double r2324353 = /* ERROR: no complex support in C */;
        double r2324354 = 0.25;
        double r2324355 = r2324350 * r2324350;
        double r2324356 = r2324354 - r2324355;
        double r2324357 = -r2324348;
        double r2324358 = r2324357 / r2324349;
        double r2324359 = /* ERROR: no complex support in C */;
        double r2324360 = 6.0;
        double r2324361 = -2.0;
        double r2324362 = r2324361 * r2324348;
        double r2324363 = r2324362 / r2324349;
        double r2324364 = /* ERROR: no complex support in C */;
        double r2324365 = r2324364 + r2324359;
        double r2324366 = r2324359 * r2324365;
        double r2324367 = r2324353 + r2324366;
        double r2324368 = /* ERROR: no complex support in C */;
        return r2324368;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(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))))