Average Error: 0 → 0
Time: 21.4s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]
↓
\[\Im(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0.0 i\right)\right)\right) + \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(\left(6 + 0.0 i\right) + \left(-1 + 1 i\right)\right)\right) + \left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(20 + 0.0 i\right)\right)\right)\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]
\Im(\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))
↓
\Im(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0.0 i\right)\right)\right) + \left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \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(\left(6 + 0.0 i\right) + \left(-1 + 1 i\right)\right)\right) + \left(\left(-1 + 1 i\right) \cdot \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(20 + 0.0 i\right)\right)\right)\right)\right)\right) + \left(1 + 0.0 i\right)\right))
double f() {
        double r10247 = -1.0;
        double r10248 = 1.0;
        double r10249 = /* ERROR: no complex support in C */;
        double r10250 = r10249 * r10249;
        double r10251 = r10250 * r10249;
        double r10252 = r10251 * r10249;
        double r10253 = r10252 * r10249;
        double r10254 = r10253 * r10249;
        double r10255 = 6.0;
        double r10256 = 0.0;
        double r10257 = /* ERROR: no complex support in C */;
        double r10258 = r10257 * r10249;
        double r10259 = r10258 * r10249;
        double r10260 = r10259 * r10249;
        double r10261 = r10260 * r10249;
        double r10262 = r10261 * r10249;
        double r10263 = r10254 + r10262;
        double r10264 = 15.0;
        double r10265 = /* ERROR: no complex support in C */;
        double r10266 = r10265 * r10249;
        double r10267 = r10266 * r10249;
        double r10268 = r10267 * r10249;
        double r10269 = r10268 * r10249;
        double r10270 = r10263 + r10269;
        double r10271 = 20.0;
        double r10272 = /* ERROR: no complex support in C */;
        double r10273 = r10272 * r10249;
        double r10274 = r10273 * r10249;
        double r10275 = r10274 * r10249;
        double r10276 = r10270 + r10275;
        double r10277 = r10276 + r10267;
        double r10278 = r10277 + r10258;
        double r10279 = /* ERROR: no complex support in C */;
        double r10280 = r10278 + r10279;
        double r10281 = /* ERROR: no complex support in C */;
        return r10281;
}
↓
double f() {
        double r10282 = -1.0;
        double r10283 = 1.0;
        double r10284 = /* ERROR: no complex support in C */;
        double r10285 = 15.0;
        double r10286 = 0.0;
        double r10287 = /* ERROR: no complex support in C */;
        double r10288 = r10287 * r10284;
        double r10289 = 6.0;
        double r10290 = /* ERROR: no complex support in C */;
        double r10291 = r10288 + r10290;
        double r10292 = r10284 * r10291;
        double r10293 = r10284 * r10284;
        double r10294 = r10293 * r10284;
        double r10295 = r10290 + r10284;
        double r10296 = r10294 * r10295;
        double r10297 = 20.0;
        double r10298 = /* ERROR: no complex support in C */;
        double r10299 = r10288 + r10298;
        double r10300 = r10284 * r10299;
        double r10301 = r10296 + r10300;
        double r10302 = r10293 * r10301;
        double r10303 = r10292 + r10302;
        double r10304 = /* ERROR: no complex support in C */;
        double r10305 = r10303 + r10304;
        double r10306 = /* ERROR: no complex support in C */;
        return r10306;
}

Error

Derivation

  1. Initial program 0

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019195 
(FPCore ()
  :name "3.9.1 imaginary part (p56)"
  (im (+ (+ (+ (+ (+ (+ (* (* (* (* (* (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))))