3.9.1 real part (p56)

Average Error: 0 → 0

Time: 24.9s

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

C

double f() {
        double r2130324 = -1.0;
        double r2130325 = 1.0;
        double r2130326 = /* ERROR: no complex support in C */;
        double r2130327 = r2130326 * r2130326;
        double r2130328 = r2130327 * r2130326;
        double r2130329 = r2130328 * r2130326;
        double r2130330 = r2130329 * r2130326;
        double r2130331 = r2130330 * r2130326;
        double r2130332 = 6.0;
        double r2130333 = 0.0;
        double r2130334 = /* ERROR: no complex support in C */;
        double r2130335 = r2130334 * r2130326;
        double r2130336 = r2130335 * r2130326;
        double r2130337 = r2130336 * r2130326;
        double r2130338 = r2130337 * r2130326;
        double r2130339 = r2130338 * r2130326;
        double r2130340 = r2130331 + r2130339;
        double r2130341 = 15.0;
        double r2130342 = /* ERROR: no complex support in C */;
        double r2130343 = r2130342 * r2130326;
        double r2130344 = r2130343 * r2130326;
        double r2130345 = r2130344 * r2130326;
        double r2130346 = r2130345 * r2130326;
        double r2130347 = r2130340 + r2130346;
        double r2130348 = 20.0;
        double r2130349 = /* ERROR: no complex support in C */;
        double r2130350 = r2130349 * r2130326;
        double r2130351 = r2130350 * r2130326;
        double r2130352 = r2130351 * r2130326;
        double r2130353 = r2130347 + r2130352;
        double r2130354 = r2130353 + r2130344;
        double r2130355 = r2130354 + r2130335;
        double r2130356 = /* ERROR: no complex support in C */;
        double r2130357 = r2130355 + r2130356;
        double r2130358 = /* ERROR: no complex support in C */;
        return r2130358;
}

↓

double f() {
        double r2130359 = 1.0;
        double r2130360 = 0.0;
        double r2130361 = /* ERROR: no complex support in C */;
        double r2130362 = -1.0;
        double r2130363 = 6.0;
        double r2130364 = r2130362 * r2130363;
        double r2130365 = r2130359 * r2130360;
        double r2130366 = r2130364 - r2130365;
        double r2130367 = r2130359 * r2130363;
        double r2130368 = r2130360 * r2130362;
        double r2130369 = r2130367 + r2130368;
        double r2130370 = /* ERROR: no complex support in C */;
        double r2130371 = r2130361 + r2130370;
        double r2130372 = r2130359 + r2130362;
        double r2130373 = r2130362 - r2130359;
        double r2130374 = r2130372 * r2130373;
        double r2130375 = r2130359 * r2130362;
        double r2130376 = r2130375 + r2130375;
        double r2130377 = /* ERROR: no complex support in C */;
        double r2130378 = 20.0;
        double r2130379 = r2130362 * r2130378;
        double r2130380 = r2130379 - r2130365;
        double r2130381 = 15.0;
        double r2130382 = r2130380 + r2130381;
        double r2130383 = r2130378 * r2130359;
        double r2130384 = r2130368 + r2130383;
        double r2130385 = r2130360 + r2130384;
        double r2130386 = /* ERROR: no complex support in C */;
        double r2130387 = r2130377 * r2130386;
        double r2130388 = r2130371 + r2130387;
        double r2130389 = /* ERROR: no complex support in C */;
        double r2130390 = r2130389 + r2130370;
        double r2130391 = r2130376 + r2130374;
        double r2130392 = r2130374 - r2130376;
        double r2130393 = r2130391 * r2130392;
        double r2130394 = r2130374 * r2130376;
        double r2130395 = r2130394 + r2130394;
        double r2130396 = /* ERROR: no complex support in C */;
        double r2130397 = r2130390 * r2130396;
        double r2130398 = r2130374 * r2130393;
        double r2130399 = r2130376 * r2130395;
        double r2130400 = r2130398 - r2130399;
        double r2130401 = r2130393 * r2130376;
        double r2130402 = r2130395 * r2130374;
        double r2130403 = r2130401 + r2130402;
        double r2130404 = /* ERROR: no complex support in C */;
        double r2130405 = r2130397 + r2130404;
        double r2130406 = r2130388 + r2130405;
        double r2130407 = /* ERROR: no complex support in C */;
        return r2130407;
}

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019172 
(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))))