Average Error: 0 → 0
Time: 21.3s
Precision: 64
\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Im(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-2 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(4 + 0 i\right)\right) + \left(7 + 0 i\right)\right))\]
\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(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \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) + \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-2 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right) + \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) + \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(4 + 0 i\right)\right) + \left(7 + 0 i\right)\right))
double f() {
        double r1402565 = 1.0;
        double r1402566 = -r1402565;
        double r1402567 = 2.0;
        double r1402568 = r1402566 / r1402567;
        double r1402569 = 3.0;
        double r1402570 = sqrt(r1402569);
        double r1402571 = r1402570 / r1402567;
        double r1402572 = /* ERROR: no complex support in C */;
        double r1402573 = r1402572 * r1402572;
        double r1402574 = r1402573 * r1402572;
        double r1402575 = r1402574 * r1402572;
        double r1402576 = -r1402567;
        double r1402577 = 0.0;
        double r1402578 = /* ERROR: no complex support in C */;
        double r1402579 = r1402578 * r1402572;
        double r1402580 = r1402579 * r1402572;
        double r1402581 = r1402580 * r1402572;
        double r1402582 = r1402575 + r1402581;
        double r1402583 = 5.0;
        double r1402584 = /* ERROR: no complex support in C */;
        double r1402585 = r1402584 * r1402572;
        double r1402586 = r1402585 * r1402572;
        double r1402587 = r1402582 + r1402586;
        double r1402588 = 4.0;
        double r1402589 = /* ERROR: no complex support in C */;
        double r1402590 = r1402589 * r1402572;
        double r1402591 = r1402587 + r1402590;
        double r1402592 = 7.0;
        double r1402593 = /* ERROR: no complex support in C */;
        double r1402594 = r1402591 + r1402593;
        double r1402595 = /* ERROR: no complex support in C */;
        return r1402595;
}
↓
double f() {
        double r1402596 = -0.5;
        double r1402597 = 3.0;
        double r1402598 = sqrt(r1402597);
        double r1402599 = 2.0;
        double r1402600 = r1402598 / r1402599;
        double r1402601 = /* ERROR: no complex support in C */;
        double r1402602 = r1402601 * r1402601;
        double r1402603 = r1402602 * r1402601;
        double r1402604 = r1402601 * r1402603;
        double r1402605 = -2.0;
        double r1402606 = 0.0;
        double r1402607 = /* ERROR: no complex support in C */;
        double r1402608 = r1402607 * r1402601;
        double r1402609 = r1402601 * r1402608;
        double r1402610 = r1402601 * r1402609;
        double r1402611 = r1402604 + r1402610;
        double r1402612 = 5.0;
        double r1402613 = /* ERROR: no complex support in C */;
        double r1402614 = r1402613 * r1402601;
        double r1402615 = r1402614 * r1402601;
        double r1402616 = r1402611 + r1402615;
        double r1402617 = 4.0;
        double r1402618 = /* ERROR: no complex support in C */;
        double r1402619 = r1402601 * r1402618;
        double r1402620 = r1402616 + r1402619;
        double r1402621 = 7.0;
        double r1402622 = /* ERROR: no complex support in C */;
        double r1402623 = r1402620 + r1402622;
        double r1402624 = /* ERROR: no complex support in C */;
        return r1402624;
}

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. Final simplification0

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

Reproduce

herbie shell --seed 2019121 
(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))))