3.9.1 imaginary part (p56)

Average Error: 0 → 0

Time: 5.3s

Precision: 64

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Math

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

↓

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

C

double f() {
        double r22234 = -1.0;
        double r22235 = 1.0;
        double r22236 = /* ERROR: no complex support in C */;
        double r22237 = r22236 * r22236;
        double r22238 = r22237 * r22236;
        double r22239 = r22238 * r22236;
        double r22240 = r22239 * r22236;
        double r22241 = r22240 * r22236;
        double r22242 = 6.0;
        double r22243 = 0.0;
        double r22244 = /* ERROR: no complex support in C */;
        double r22245 = r22244 * r22236;
        double r22246 = r22245 * r22236;
        double r22247 = r22246 * r22236;
        double r22248 = r22247 * r22236;
        double r22249 = r22248 * r22236;
        double r22250 = r22241 + r22249;
        double r22251 = 15.0;
        double r22252 = /* ERROR: no complex support in C */;
        double r22253 = r22252 * r22236;
        double r22254 = r22253 * r22236;
        double r22255 = r22254 * r22236;
        double r22256 = r22255 * r22236;
        double r22257 = r22250 + r22256;
        double r22258 = 20.0;
        double r22259 = /* ERROR: no complex support in C */;
        double r22260 = r22259 * r22236;
        double r22261 = r22260 * r22236;
        double r22262 = r22261 * r22236;
        double r22263 = r22257 + r22262;
        double r22264 = r22263 + r22254;
        double r22265 = r22264 + r22245;
        double r22266 = /* ERROR: no complex support in C */;
        double r22267 = r22265 + r22266;
        double r22268 = /* ERROR: no complex support in C */;
        return r22268;
}

↓

double f() {
        double r22269 = -1.0;
        double r22270 = 1.0;
        double r22271 = /* ERROR: no complex support in C */;
        double r22272 = 20.0;
        double r22273 = 0.0;
        double r22274 = /* ERROR: no complex support in C */;
        double r22275 = r22274 * r22271;
        double r22276 = 15.0;
        double r22277 = /* ERROR: no complex support in C */;
        double r22278 = r22275 + r22277;
        double r22279 = r22271 * r22278;
        double r22280 = 6.0;
        double r22281 = /* ERROR: no complex support in C */;
        double r22282 = r22279 + r22281;
        double r22283 = r22271 * r22282;
        double r22284 = /* ERROR: no complex support in C */;
        double r22285 = r22283 + r22284;
        double r22286 = r22271 * r22271;
        double r22287 = r22277 * r22271;
        double r22288 = r22271 + r22281;
        double r22289 = r22286 * r22288;
        double r22290 = r22287 + r22289;
        double r22291 = r22286 * r22290;
        double r22292 = r22271 * r22291;
        double r22293 = r22285 + r22292;
        double r22294 = /* ERROR: no complex support in C */;
        return r22294;
}

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. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore ()
  :name "3.9.1 imaginary part (p56)"
  :precision binary64
  (im (+ (+ (+ (+ (+ (+ (* (* (* (* (* (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (* (* (* (* (* (complex 6 0.0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (* (* (complex 15 0.0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (* (complex 20 0.0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (* (* (complex 15 0.0) (complex -1 1)) (complex -1 1))) (* (complex 6 0.0) (complex -1 1))) (complex 1 0.0))))