Average Error: 61.9 → 0
Time: 23.7s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\frac{11}{2} + \left(\left(-\sqrt{3}\right) - \frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]
\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{11}{2} + \left(\left(-\sqrt{3}\right) - \frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))
double f() {
        double r807385 = 1.0;
        double r807386 = -r807385;
        double r807387 = 2.0;
        double r807388 = r807386 / r807387;
        double r807389 = 3.0;
        double r807390 = sqrt(r807389);
        double r807391 = r807390 / r807387;
        double r807392 = /* ERROR: no complex support in C */;
        double r807393 = r807392 * r807392;
        double r807394 = r807393 * r807392;
        double r807395 = r807394 * r807392;
        double r807396 = -r807387;
        double r807397 = 0.0;
        double r807398 = /* ERROR: no complex support in C */;
        double r807399 = r807398 * r807392;
        double r807400 = r807399 * r807392;
        double r807401 = r807400 * r807392;
        double r807402 = r807395 + r807401;
        double r807403 = 5.0;
        double r807404 = /* ERROR: no complex support in C */;
        double r807405 = r807404 * r807392;
        double r807406 = r807405 * r807392;
        double r807407 = r807402 + r807406;
        double r807408 = 4.0;
        double r807409 = /* ERROR: no complex support in C */;
        double r807410 = r807409 * r807392;
        double r807411 = r807407 + r807410;
        double r807412 = 7.0;
        double r807413 = /* ERROR: no complex support in C */;
        double r807414 = r807411 + r807413;
        double r807415 = /* ERROR: no complex support in C */;
        return r807415;
}
↓
double f() {
        double r807416 = 5.5;
        double r807417 = 3.0;
        double r807418 = sqrt(r807417);
        double r807419 = -r807418;
        double r807420 = 2.0;
        double r807421 = r807418 / r807420;
        double r807422 = r807419 - r807421;
        double r807423 = /* ERROR: no complex support in C */;
        double r807424 = -0.5;
        double r807425 = -2.0;
        double r807426 = r807418 / r807425;
        double r807427 = /* ERROR: no complex support in C */;
        double r807428 = r807423 * r807427;
        double r807429 = 5.0;
        double r807430 = r807418 * r807420;
        double r807431 = /* ERROR: no complex support in C */;
        double r807432 = r807428 + r807431;
        double r807433 = /* ERROR: no complex support in C */;
        return r807433;
}

Error

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. Simplified0

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

  3. Final simplification0

    \[\leadsto \Re(\left(\left(\frac{11}{2} + \left(\left(-\sqrt{3}\right) - \frac{\sqrt{3}}{2}\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]

Reproduce

herbie shell --seed 2019151 
(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))))