3.9.1 real part (p56)

Average Error: 0 → 0

Time: 24.8s

Precision: 64

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

↓

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(1 + -1\right) \cdot 15\right) \cdot \left(-1 - 1\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot 0.0\right) + \left(-1 \cdot 6 - 1 \cdot 0.0\right)\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) - \left(0.0 \cdot -1 + 1 \cdot 6\right) \cdot \left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right)\right)\right) + \left(\left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(0.0 \cdot -1 + 1 \cdot 6\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(\left(0.0 \cdot -1 + 1 \cdot 6\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 0.0 + \left(\left(-1 + -1\right) \cdot 1\right) \cdot 15\right)\right)\right) i\right) + \left(\left(\left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(\left(20 \cdot -1 - 1 \cdot 0.0\right) + \left(\left(\left(1 + -1\right) \cdot 15\right) \cdot \left(-1 - 1\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot 0.0\right)\right)\right) + \left(\left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 0.0 + \left(\left(-1 + -1\right) \cdot 1\right) \cdot 15\right) + \left(20 \cdot 1 + 0.0 \cdot -1\right)\right)\right) i\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) + \left(-1 + -1\right) \cdot 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

C

double f() {
        double r3478242 = -1.0;
        double r3478243 = 1.0;
        double r3478244 = /* ERROR: no complex support in C */;
        double r3478245 = r3478244 * r3478244;
        double r3478246 = r3478245 * r3478244;
        double r3478247 = r3478246 * r3478244;
        double r3478248 = r3478247 * r3478244;
        double r3478249 = r3478248 * r3478244;
        double r3478250 = 6.0;
        double r3478251 = 0.0;
        double r3478252 = /* ERROR: no complex support in C */;
        double r3478253 = r3478252 * r3478244;
        double r3478254 = r3478253 * r3478244;
        double r3478255 = r3478254 * r3478244;
        double r3478256 = r3478255 * r3478244;
        double r3478257 = r3478256 * r3478244;
        double r3478258 = r3478249 + r3478257;
        double r3478259 = 15.0;
        double r3478260 = /* ERROR: no complex support in C */;
        double r3478261 = r3478260 * r3478244;
        double r3478262 = r3478261 * r3478244;
        double r3478263 = r3478262 * r3478244;
        double r3478264 = r3478263 * r3478244;
        double r3478265 = r3478258 + r3478264;
        double r3478266 = 20.0;
        double r3478267 = /* ERROR: no complex support in C */;
        double r3478268 = r3478267 * r3478244;
        double r3478269 = r3478268 * r3478244;
        double r3478270 = r3478269 * r3478244;
        double r3478271 = r3478265 + r3478270;
        double r3478272 = r3478271 + r3478262;
        double r3478273 = r3478272 + r3478253;
        double r3478274 = /* ERROR: no complex support in C */;
        double r3478275 = r3478273 + r3478274;
        double r3478276 = /* ERROR: no complex support in C */;
        return r3478276;
}

↓

double f() {
        double r3478277 = 1.0;
        double r3478278 = -1.0;
        double r3478279 = r3478277 + r3478278;
        double r3478280 = 15.0;
        double r3478281 = r3478279 * r3478280;
        double r3478282 = r3478278 - r3478277;
        double r3478283 = r3478281 * r3478282;
        double r3478284 = r3478278 + r3478278;
        double r3478285 = r3478284 * r3478277;
        double r3478286 = 0.0;
        double r3478287 = r3478285 * r3478286;
        double r3478288 = r3478283 - r3478287;
        double r3478289 = 6.0;
        double r3478290 = r3478278 * r3478289;
        double r3478291 = r3478277 * r3478286;
        double r3478292 = r3478290 - r3478291;
        double r3478293 = r3478288 + r3478292;
        double r3478294 = r3478279 * r3478282;
        double r3478295 = r3478294 * r3478294;
        double r3478296 = r3478285 * r3478285;
        double r3478297 = r3478295 - r3478296;
        double r3478298 = r3478292 * r3478297;
        double r3478299 = r3478286 * r3478278;
        double r3478300 = r3478277 * r3478289;
        double r3478301 = r3478299 + r3478300;
        double r3478302 = r3478279 * r3478285;
        double r3478303 = r3478282 * r3478302;
        double r3478304 = r3478303 + r3478303;
        double r3478305 = r3478301 * r3478304;
        double r3478306 = r3478298 - r3478305;
        double r3478307 = r3478293 + r3478306;
        double r3478308 = r3478292 * r3478304;
        double r3478309 = r3478301 * r3478297;
        double r3478310 = r3478308 + r3478309;
        double r3478311 = r3478294 * r3478286;
        double r3478312 = r3478285 * r3478280;
        double r3478313 = r3478311 + r3478312;
        double r3478314 = r3478301 + r3478313;
        double r3478315 = r3478310 + r3478314;
        double r3478316 = /* ERROR: no complex support in C */;
        double r3478317 = 20.0;
        double r3478318 = r3478317 * r3478278;
        double r3478319 = r3478318 - r3478291;
        double r3478320 = r3478319 + r3478288;
        double r3478321 = r3478297 + r3478320;
        double r3478322 = r3478317 * r3478277;
        double r3478323 = r3478322 + r3478299;
        double r3478324 = r3478313 + r3478323;
        double r3478325 = r3478304 + r3478324;
        double r3478326 = /* ERROR: no complex support in C */;
        double r3478327 = /* ERROR: no complex support in C */;
        double r3478328 = r3478326 * r3478327;
        double r3478329 = r3478316 + r3478328;
        double r3478330 = /* ERROR: no complex support in C */;
        double r3478331 = r3478329 + r3478330;
        double r3478332 = /* ERROR: no complex support in C */;
        return r3478332;
}

Derivation

1. Initial program 0

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Re(\left(\left(\left(\left(\left(\left(\left(15 \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) - 0.0 \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right) + \left(-1 \cdot 6 - 1 \cdot 0.0\right)\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) - \left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right) - \left(6 \cdot 1 + 0.0 \cdot -1\right) \cdot \left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) + \left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right)\right)\right)\right) + \left(\left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot 15 + \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot 0.0\right) + \left(6 \cdot 1 + 0.0 \cdot -1\right)\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) + \left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right)\right) + \left(6 \cdot 1 + 0.0 \cdot -1\right) \cdot \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) - \left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right)\right)\right) i\right) + \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right) + 1 \cdot \left(-1 + -1\right) i\right) \cdot \left(\left(\left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) - \left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right) + \left(\left(\left(15 \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) - 0.0 \cdot \left(1 \cdot \left(-1 + -1\right)\right)\right) + \left(-1 \cdot 20 - 1 \cdot 0.0\right)\right)\right) + \left(\left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right) + \left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 - 1\right)\right) + \left(\left(\left(1 \cdot \left(-1 + -1\right)\right) \cdot 15 + \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot 0.0\right) + \left(1 \cdot 20 + 0.0 \cdot -1\right)\right)\right) i\right)\right)\right) + \left(1 + 0.0 i\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(\left(\left(\left(\left(\left(\left(1 + -1\right) \cdot 15\right) \cdot \left(-1 - 1\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot 0.0\right) + \left(-1 \cdot 6 - 1 \cdot 0.0\right)\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) - \left(0.0 \cdot -1 + 1 \cdot 6\right) \cdot \left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right)\right)\right) + \left(\left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) \cdot \left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(0.0 \cdot -1 + 1 \cdot 6\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(\left(0.0 \cdot -1 + 1 \cdot 6\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 0.0 + \left(\left(-1 + -1\right) \cdot 1\right) \cdot 15\right)\right)\right) i\right) + \left(\left(\left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(\left(20 \cdot -1 - 1 \cdot 0.0\right) + \left(\left(\left(1 + -1\right) \cdot 15\right) \cdot \left(-1 - 1\right) - \left(\left(-1 + -1\right) \cdot 1\right) \cdot 0.0\right)\right)\right) + \left(\left(\left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right) + \left(-1 - 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(\left(-1 + -1\right) \cdot 1\right)\right)\right) + \left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 0.0 + \left(\left(-1 + -1\right) \cdot 1\right) \cdot 15\right) + \left(20 \cdot 1 + 0.0 \cdot -1\right)\right)\right) i\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) + \left(-1 + -1\right) \cdot 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

Reproduce

herbie shell --seed 2019192 
(FPCore ()
  :name "3.9.1 real part (p56)"
  (re (+ (+ (+ (+ (+ (+ (* (* (* (* (* (complex -1.0 1.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (* (* (* (* (* (complex 6.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (* (* (complex 15.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (* (complex 20.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (complex 15.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (complex 6.0 0.0) (complex -1.0 1.0))) (complex 1.0 0.0))))