3.9.2 imaginary part (p56)

Average Error: 0 → 0

Time: 29.0s

Precision: 64

Math

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

↓

\[\Im(\left(\left(-5 + \left(\left(\frac{-\sqrt{3}}{-4} + \frac{-\sqrt{3}}{-4}\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(10 \cdot \frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{2}\right)\right)\right) i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

C

double f() {
        double r1336369 = 1.0;
        double r1336370 = -r1336369;
        double r1336371 = 2.0;
        double r1336372 = r1336370 / r1336371;
        double r1336373 = 3.0;
        double r1336374 = sqrt(r1336373);
        double r1336375 = r1336374 / r1336371;
        double r1336376 = /* ERROR: no complex support in C */;
        double r1336377 = r1336376 * r1336376;
        double r1336378 = r1336377 * r1336376;
        double r1336379 = r1336378 * r1336376;
        double r1336380 = -r1336371;
        double r1336381 = 0.0;
        double r1336382 = /* ERROR: no complex support in C */;
        double r1336383 = r1336382 * r1336376;
        double r1336384 = r1336383 * r1336376;
        double r1336385 = r1336384 * r1336376;
        double r1336386 = r1336379 + r1336385;
        double r1336387 = 5.0;
        double r1336388 = /* ERROR: no complex support in C */;
        double r1336389 = r1336388 * r1336376;
        double r1336390 = r1336389 * r1336376;
        double r1336391 = r1336386 + r1336390;
        double r1336392 = 4.0;
        double r1336393 = /* ERROR: no complex support in C */;
        double r1336394 = r1336393 * r1336376;
        double r1336395 = r1336391 + r1336394;
        double r1336396 = 7.0;
        double r1336397 = /* ERROR: no complex support in C */;
        double r1336398 = r1336395 + r1336397;
        double r1336399 = /* ERROR: no complex support in C */;
        return r1336399;
}

↓

double f() {
        double r1336400 = -5.0;
        double r1336401 = 3.0;
        double r1336402 = sqrt(r1336401);
        double r1336403 = -r1336402;
        double r1336404 = -4.0;
        double r1336405 = r1336403 / r1336404;
        double r1336406 = r1336405 + r1336405;
        double r1336407 = r1336402 / r1336404;
        double r1336408 = r1336407 + r1336407;
        double r1336409 = 10.0;
        double r1336410 = r1336409 * r1336407;
        double r1336411 = 2.0;
        double r1336412 = r1336402 / r1336411;
        double r1336413 = r1336410 + r1336412;
        double r1336414 = r1336408 + r1336413;
        double r1336415 = r1336406 + r1336414;
        double r1336416 = /* ERROR: no complex support in C */;
        double r1336417 = 5.0;
        double r1336418 = r1336402 * r1336411;
        double r1336419 = /* ERROR: no complex support in C */;
        double r1336420 = r1336416 + r1336419;
        double r1336421 = /* ERROR: no complex support in C */;
        return r1336421;
}

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. Simplified 0

   \[\leadsto \color{blue}{\Im(\left(\left(5 + 2 \cdot \sqrt{3} i\right) + \left(-5 + \left(\left(\left(-\frac{\sqrt{3}}{-4}\right) + \left(-\frac{\sqrt{3}}{-4}\right)\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{-4} \cdot 10\right)\right)\right) i\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Im(\left(\left(-5 + \left(\left(\frac{-\sqrt{3}}{-4} + \frac{-\sqrt{3}}{-4}\right) + \left(\left(\frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{-4}\right) + \left(10 \cdot \frac{\sqrt{3}}{-4} + \frac{\sqrt{3}}{2}\right)\right)\right) i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

Reproduce

herbie shell --seed 2019132 
(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))))