Average Error: 0 → 0
Time: 21.6s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(\left(7 - \frac{4}{2}\right) + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(5 + \left(1 + \left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right)\right) + \left(\left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) + \frac{\sqrt{3}}{2} \cdot \left(-2\right)\right) i\right) \cdot \left(\left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) i\right)\right))\]
\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))
↓
\Im(\left(\left(\left(7 - \frac{4}{2}\right) + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(5 + \left(1 + \left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right)\right) + \left(\left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) + \frac{\sqrt{3}}{2} \cdot \left(-2\right)\right) i\right) \cdot \left(\left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) i\right)\right))
double f() {
        double r1657286 = 1.0;
        double r1657287 = -r1657286;
        double r1657288 = 2.0;
        double r1657289 = r1657287 / r1657288;
        double r1657290 = 3.0;
        double r1657291 = sqrt(r1657290);
        double r1657292 = r1657291 / r1657288;
        double r1657293 = /* ERROR: no complex support in C */;
        double r1657294 = r1657293 * r1657293;
        double r1657295 = r1657294 * r1657293;
        double r1657296 = r1657295 * r1657293;
        double r1657297 = -r1657288;
        double r1657298 = 0.0;
        double r1657299 = /* ERROR: no complex support in C */;
        double r1657300 = r1657299 * r1657293;
        double r1657301 = r1657300 * r1657293;
        double r1657302 = r1657301 * r1657293;
        double r1657303 = r1657296 + r1657302;
        double r1657304 = 5.0;
        double r1657305 = /* ERROR: no complex support in C */;
        double r1657306 = r1657305 * r1657293;
        double r1657307 = r1657306 * r1657293;
        double r1657308 = r1657303 + r1657307;
        double r1657309 = 4.0;
        double r1657310 = /* ERROR: no complex support in C */;
        double r1657311 = r1657310 * r1657293;
        double r1657312 = r1657308 + r1657311;
        double r1657313 = 7.0;
        double r1657314 = /* ERROR: no complex support in C */;
        double r1657315 = r1657312 + r1657314;
        double r1657316 = /* ERROR: no complex support in C */;
        return r1657316;
}
↓
double f() {
        double r1657317 = 7.0;
        double r1657318 = 4.0;
        double r1657319 = 2.0;
        double r1657320 = r1657318 / r1657319;
        double r1657321 = r1657317 - r1657320;
        double r1657322 = 3.0;
        double r1657323 = sqrt(r1657322);
        double r1657324 = r1657323 / r1657319;
        double r1657325 = r1657318 * r1657324;
        double r1657326 = /* ERROR: no complex support in C */;
        double r1657327 = 5.0;
        double r1657328 = 1.0;
        double r1657329 = r1657328 / r1657319;
        double r1657330 = r1657329 / r1657319;
        double r1657331 = r1657324 * r1657324;
        double r1657332 = r1657330 - r1657331;
        double r1657333 = r1657328 + r1657332;
        double r1657334 = r1657327 + r1657333;
        double r1657335 = r1657324 / r1657319;
        double r1657336 = r1657335 + r1657335;
        double r1657337 = -r1657336;
        double r1657338 = -r1657319;
        double r1657339 = r1657324 * r1657338;
        double r1657340 = r1657337 + r1657339;
        double r1657341 = /* ERROR: no complex support in C */;
        double r1657342 = /* ERROR: no complex support in C */;
        double r1657343 = r1657341 * r1657342;
        double r1657344 = r1657326 + r1657343;
        double r1657345 = /* ERROR: no complex support in C */;
        return r1657345;
}

Error

Derivation

  1. Initial program 0

    \[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

  2. Simplified0

    \[\leadsto \color{blue}{\Im(\left(\left(\left(7 - \frac{4}{2}\right) + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(5 + \left(1 + \left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right)\right) + \left(-\left(2 \cdot \frac{\sqrt{3}}{2} + \left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right)\right) i\right) \cdot \left(\left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) i\right)\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Im(\left(\left(\left(7 - \frac{4}{2}\right) + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(5 + \left(1 + \left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right)\right)\right) + \left(\left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) + \frac{\sqrt{3}}{2} \cdot \left(-2\right)\right) i\right) \cdot \left(\left(\frac{\frac{1}{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \left(-\left(\frac{\frac{\sqrt{3}}{2}}{2} + \frac{\frac{\sqrt{3}}{2}}{2}\right)\right) i\right)\right))\]

Reproduce

herbie shell --seed 2019134 
(FPCore ()
  :name "3.9.2 imaginary part (p56)"
  (im (+.c (+.c (+.c (+.c (*.c (*.c (*.c (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (*.c (*.c (*.c (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (*.c (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))