3.9.1 imaginary part (p56)

Average Error: 0 → 0

Time: 5.7s

Precision: 64

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Math

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

↓

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

C

double f() {
        double r36302 = -1.0;
        double r36303 = 1.0;
        double r36304 = /* ERROR: no complex support in C */;
        double r36305 = r36304 * r36304;
        double r36306 = r36305 * r36304;
        double r36307 = r36306 * r36304;
        double r36308 = r36307 * r36304;
        double r36309 = r36308 * r36304;
        double r36310 = 6.0;
        double r36311 = 0.0;
        double r36312 = /* ERROR: no complex support in C */;
        double r36313 = r36312 * r36304;
        double r36314 = r36313 * r36304;
        double r36315 = r36314 * r36304;
        double r36316 = r36315 * r36304;
        double r36317 = r36316 * r36304;
        double r36318 = r36309 + r36317;
        double r36319 = 15.0;
        double r36320 = /* ERROR: no complex support in C */;
        double r36321 = r36320 * r36304;
        double r36322 = r36321 * r36304;
        double r36323 = r36322 * r36304;
        double r36324 = r36323 * r36304;
        double r36325 = r36318 + r36324;
        double r36326 = 20.0;
        double r36327 = /* ERROR: no complex support in C */;
        double r36328 = r36327 * r36304;
        double r36329 = r36328 * r36304;
        double r36330 = r36329 * r36304;
        double r36331 = r36325 + r36330;
        double r36332 = r36331 + r36322;
        double r36333 = r36332 + r36313;
        double r36334 = /* ERROR: no complex support in C */;
        double r36335 = r36333 + r36334;
        double r36336 = /* ERROR: no complex support in C */;
        return r36336;
}

↓

double f() {
        double r36337 = -1.0;
        double r36338 = 1.0;
        double r36339 = /* ERROR: no complex support in C */;
        double r36340 = r36339 * r36339;
        double r36341 = 15.0;
        double r36342 = 0.0;
        double r36343 = /* ERROR: no complex support in C */;
        double r36344 = r36343 * r36339;
        double r36345 = 6.0;
        double r36346 = /* ERROR: no complex support in C */;
        double r36347 = r36339 + r36346;
        double r36348 = r36340 * r36347;
        double r36349 = r36344 + r36348;
        double r36350 = r36340 * r36349;
        double r36351 = r36339 * r36350;
        double r36352 = 20.0;
        double r36353 = /* ERROR: no complex support in C */;
        double r36354 = r36353 * r36339;
        double r36355 = r36354 + r36343;
        double r36356 = r36339 * r36355;
        double r36357 = r36356 + r36346;
        double r36358 = r36339 * r36357;
        double r36359 = r36351 + r36358;
        double r36360 = /* ERROR: no complex support in C */;
        double r36361 = r36359 + r36360;
        double r36362 = /* ERROR: no complex support in C */;
        return r36362;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019350 +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))))