3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 20.7s

Precision: 64

Math

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

↓

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

C

double f() {
        double r1033565 = 1.0;
        double r1033566 = -r1033565;
        double r1033567 = 2.0;
        double r1033568 = r1033566 / r1033567;
        double r1033569 = 3.0;
        double r1033570 = sqrt(r1033569);
        double r1033571 = r1033570 / r1033567;
        double r1033572 = /* ERROR: no complex support in C */;
        double r1033573 = r1033572 * r1033572;
        double r1033574 = r1033573 * r1033572;
        double r1033575 = r1033574 * r1033572;
        double r1033576 = -r1033567;
        double r1033577 = 0.0;
        double r1033578 = /* ERROR: no complex support in C */;
        double r1033579 = r1033578 * r1033572;
        double r1033580 = r1033579 * r1033572;
        double r1033581 = r1033580 * r1033572;
        double r1033582 = r1033575 + r1033581;
        double r1033583 = 5.0;
        double r1033584 = /* ERROR: no complex support in C */;
        double r1033585 = r1033584 * r1033572;
        double r1033586 = r1033585 * r1033572;
        double r1033587 = r1033582 + r1033586;
        double r1033588 = 4.0;
        double r1033589 = /* ERROR: no complex support in C */;
        double r1033590 = r1033589 * r1033572;
        double r1033591 = r1033587 + r1033590;
        double r1033592 = 7.0;
        double r1033593 = /* ERROR: no complex support in C */;
        double r1033594 = r1033591 + r1033593;
        double r1033595 = /* ERROR: no complex support in C */;
        return r1033595;
}

↓

double f() {
        double r1033596 = 2.5;
        double r1033597 = 3.0;
        double r1033598 = sqrt(r1033597);
        double r1033599 = -0.8;
        double r1033600 = r1033598 / r1033599;
        double r1033601 = 2.0;
        double r1033602 = r1033598 * r1033601;
        double r1033603 = r1033600 + r1033602;
        double r1033604 = r1033603 + r1033600;
        double r1033605 = /* ERROR: no complex support in C */;
        double r1033606 = -0.5;
        double r1033607 = r1033598 / r1033601;
        double r1033608 = /* ERROR: no complex support in C */;
        double r1033609 = -2.0;
        double r1033610 = -r1033598;
        double r1033611 = r1033610 / r1033601;
        double r1033612 = r1033607 + r1033611;
        double r1033613 = /* ERROR: no complex support in C */;
        double r1033614 = r1033608 + r1033613;
        double r1033615 = r1033605 + r1033614;
        double r1033616 = /* ERROR: no complex support in C */;
        return r1033616;
}

Derivation

1. Initial program 61.9

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

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019129 
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+.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))))