3.9.2 imaginary part (p56)

Average Error: 0 → 0

Time: 20.8s

Precision: 64

Math

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

↓

\[\Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\left(\left(-\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{1}{4}\right) + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{\sqrt{3}}{-1} i\right)\right) \cdot \left(\left(\left(-\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{1}{4}\right) + \frac{-\sqrt{3}}{2} i\right)\right))\]

C

double f() {
        double r754550 = 1.0;
        double r754551 = -r754550;
        double r754552 = 2.0;
        double r754553 = r754551 / r754552;
        double r754554 = 3.0;
        double r754555 = sqrt(r754554);
        double r754556 = r754555 / r754552;
        double r754557 = /* ERROR: no complex support in C */;
        double r754558 = r754557 * r754557;
        double r754559 = r754558 * r754557;
        double r754560 = r754559 * r754557;
        double r754561 = -r754552;
        double r754562 = 0.0;
        double r754563 = /* ERROR: no complex support in C */;
        double r754564 = r754563 * r754557;
        double r754565 = r754564 * r754557;
        double r754566 = r754565 * r754557;
        double r754567 = r754560 + r754566;
        double r754568 = 5.0;
        double r754569 = /* ERROR: no complex support in C */;
        double r754570 = r754569 * r754557;
        double r754571 = r754570 * r754557;
        double r754572 = r754567 + r754571;
        double r754573 = 4.0;
        double r754574 = /* ERROR: no complex support in C */;
        double r754575 = r754574 * r754557;
        double r754576 = r754572 + r754575;
        double r754577 = 7.0;
        double r754578 = /* ERROR: no complex support in C */;
        double r754579 = r754576 + r754578;
        double r754580 = /* ERROR: no complex support in C */;
        return r754580;
}

↓

double f() {
        double r754581 = 5.0;
        double r754582 = 3.0;
        double r754583 = sqrt(r754582);
        double r754584 = 2.0;
        double r754585 = r754583 / r754584;
        double r754586 = 4.0;
        double r754587 = r754585 * r754586;
        double r754588 = /* ERROR: no complex support in C */;
        double r754589 = r754585 * r754585;
        double r754590 = -r754589;
        double r754591 = 0.25;
        double r754592 = r754590 + r754591;
        double r754593 = -r754583;
        double r754594 = r754593 / r754584;
        double r754595 = /* ERROR: no complex support in C */;
        double r754596 = 6.0;
        double r754597 = -1.0;
        double r754598 = r754583 / r754597;
        double r754599 = /* ERROR: no complex support in C */;
        double r754600 = r754595 + r754599;
        double r754601 = r754600 * r754595;
        double r754602 = r754588 + r754601;
        double r754603 = /* ERROR: no complex support in C */;
        return r754603;
}

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

   \[\leadsto \color{blue}{\Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\left(\frac{1}{4} + \left(-\frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\left(6 + 1 \cdot \frac{\sqrt{3}}{-1} i\right) + \left(\left(\frac{1}{4} + \left(-\frac{\sqrt{3}}{2}\right) \cdot \frac{\sqrt{3}}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) i\right)\right)\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\left(\left(-\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{1}{4}\right) + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{\sqrt{3}}{-1} i\right)\right) \cdot \left(\left(\left(-\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{1}{4}\right) + \frac{-\sqrt{3}}{2} i\right)\right))\]

Reproduce

herbie shell --seed 2019152 
(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))))