3.9.1 real part (p56)

Average Error: 0 → 0

Time: 1.8m

Precision: 64

Math

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

↓

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

C

double f() {
        double r1016234 = -1.0;
        double r1016235 = 1.0;
        double r1016236 = /* ERROR: no complex support in C */;
        double r1016237 = r1016236 * r1016236;
        double r1016238 = r1016237 * r1016236;
        double r1016239 = r1016238 * r1016236;
        double r1016240 = r1016239 * r1016236;
        double r1016241 = r1016240 * r1016236;
        double r1016242 = 6.0;
        double r1016243 = 0.0;
        double r1016244 = /* ERROR: no complex support in C */;
        double r1016245 = r1016244 * r1016236;
        double r1016246 = r1016245 * r1016236;
        double r1016247 = r1016246 * r1016236;
        double r1016248 = r1016247 * r1016236;
        double r1016249 = r1016248 * r1016236;
        double r1016250 = r1016241 + r1016249;
        double r1016251 = 15.0;
        double r1016252 = /* ERROR: no complex support in C */;
        double r1016253 = r1016252 * r1016236;
        double r1016254 = r1016253 * r1016236;
        double r1016255 = r1016254 * r1016236;
        double r1016256 = r1016255 * r1016236;
        double r1016257 = r1016250 + r1016256;
        double r1016258 = 20.0;
        double r1016259 = /* ERROR: no complex support in C */;
        double r1016260 = r1016259 * r1016236;
        double r1016261 = r1016260 * r1016236;
        double r1016262 = r1016261 * r1016236;
        double r1016263 = r1016257 + r1016262;
        double r1016264 = r1016263 + r1016254;
        double r1016265 = r1016264 + r1016245;
        double r1016266 = /* ERROR: no complex support in C */;
        double r1016267 = r1016265 + r1016266;
        double r1016268 = /* ERROR: no complex support in C */;
        return r1016268;
}

↓

double f() {
        double r1016269 = 1.0;
        double r1016270 = 6.0;
        double r1016271 = -1.0;
        double r1016272 = r1016270 * r1016271;
        double r1016273 = 0.0;
        double r1016274 = r1016273 * r1016269;
        double r1016275 = r1016272 - r1016274;
        double r1016276 = r1016269 + r1016275;
        double r1016277 = r1016269 * r1016270;
        double r1016278 = r1016273 + r1016277;
        double r1016279 = r1016273 * r1016271;
        double r1016280 = r1016278 + r1016279;
        double r1016281 = /* ERROR: no complex support in C */;
        double r1016282 = r1016271 - r1016269;
        double r1016283 = r1016269 + r1016271;
        double r1016284 = r1016282 * r1016283;
        double r1016285 = r1016269 + r1016269;
        double r1016286 = r1016285 * r1016271;
        double r1016287 = /* ERROR: no complex support in C */;
        double r1016288 = 15.0;
        double r1016289 = r1016288 + r1016275;
        double r1016290 = /* ERROR: no complex support in C */;
        double r1016291 = r1016287 * r1016290;
        double r1016292 = 20.0;
        double r1016293 = r1016292 * r1016271;
        double r1016294 = r1016293 - r1016274;
        double r1016295 = r1016292 * r1016269;
        double r1016296 = r1016295 + r1016279;
        double r1016297 = /* ERROR: no complex support in C */;
        double r1016298 = /* ERROR: no complex support in C */;
        double r1016299 = r1016297 + r1016298;
        double r1016300 = r1016291 + r1016299;
        double r1016301 = r1016300 * r1016287;
        double r1016302 = r1016284 * r1016271;
        double r1016303 = r1016269 * r1016286;
        double r1016304 = r1016302 - r1016303;
        double r1016305 = r1016304 * r1016304;
        double r1016306 = r1016284 * r1016269;
        double r1016307 = r1016271 * r1016286;
        double r1016308 = r1016306 + r1016307;
        double r1016309 = r1016308 * r1016308;
        double r1016310 = r1016305 - r1016309;
        double r1016311 = r1016304 * r1016308;
        double r1016312 = r1016311 + r1016311;
        double r1016313 = /* ERROR: no complex support in C */;
        double r1016314 = r1016301 + r1016313;
        double r1016315 = r1016281 + r1016314;
        double r1016316 = /* ERROR: no complex support in C */;
        return r1016316;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019200 
(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))))