Average Error: 0 → 0
Time: 23.4s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right) + \left(\left(\left(\left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(20 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(1 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(-5 + -24 i\right) + \left(\left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right) + \left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right)\right)\right))\]
double f() {
        double r2052514 = -1.0;
        double r2052515 = 1.0;
        double r2052516 = /* ERROR: no complex support in C */;
        double r2052517 = r2052516 * r2052516;
        double r2052518 = r2052517 * r2052516;
        double r2052519 = r2052518 * r2052516;
        double r2052520 = r2052519 * r2052516;
        double r2052521 = r2052520 * r2052516;
        double r2052522 = 6.0;
        double r2052523 = 0.0;
        double r2052524 = /* ERROR: no complex support in C */;
        double r2052525 = r2052524 * r2052516;
        double r2052526 = r2052525 * r2052516;
        double r2052527 = r2052526 * r2052516;
        double r2052528 = r2052527 * r2052516;
        double r2052529 = r2052528 * r2052516;
        double r2052530 = r2052521 + r2052529;
        double r2052531 = 15.0;
        double r2052532 = /* ERROR: no complex support in C */;
        double r2052533 = r2052532 * r2052516;
        double r2052534 = r2052533 * r2052516;
        double r2052535 = r2052534 * r2052516;
        double r2052536 = r2052535 * r2052516;
        double r2052537 = r2052530 + r2052536;
        double r2052538 = 20.0;
        double r2052539 = /* ERROR: no complex support in C */;
        double r2052540 = r2052539 * r2052516;
        double r2052541 = r2052540 * r2052516;
        double r2052542 = r2052541 * r2052516;
        double r2052543 = r2052537 + r2052542;
        double r2052544 = r2052543 + r2052534;
        double r2052545 = r2052544 + r2052525;
        double r2052546 = /* ERROR: no complex support in C */;
        double r2052547 = r2052545 + r2052546;
        double r2052548 = /* ERROR: no complex support in C */;
        return r2052548;
}
↓
double f() {
        double r2052549 = -5.0;
        double r2052550 = -24.0;
        double r2052551 = /* ERROR: no complex support in C */;
        double r2052552 = 24.0;
        double r2052553 = /* ERROR: no complex support in C */;
        double r2052554 = 0.0;
        double r2052555 = 8.0;
        double r2052556 = /* ERROR: no complex support in C */;
        double r2052557 = r2052553 + r2052556;
        double r2052558 = 40.0;
        double r2052559 = /* ERROR: no complex support in C */;
        double r2052560 = -60.0;
        double r2052561 = /* ERROR: no complex support in C */;
        double r2052562 = r2052559 + r2052561;
        double r2052563 = r2052557 + r2052562;
        double r2052564 = r2052551 + r2052563;
        double r2052565 = /* ERROR: no complex support in C */;
        return r2052565;
}


\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right) + \left(\left(\left(\left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(20 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) + \left(1 + 0 i\right)\right))
↓
\Re(\left(\left(-5 + -24 i\right) + \left(\left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right) + \left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right)\right)\right))

Error

Derivation

  1. Initial program 0

    \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0 i\right)\right))\]

  2. Simplified0

    \[\leadsto \color{blue}{\Re(\left(\left(-5 + -24 i\right) + \left(\left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right) + \left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right)\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(-5 + -24 i\right) + \left(\left(\left(24 + -24 i\right) + \left(0 + 8 i\right)\right) + \left(\left(40 + 40 i\right) + \left(-60 + 0 i\right)\right)\right)\right))\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore ()
  :name "3.9.1 real part (p56)"
  (re (+.c (+.c (+.c (+.c (+.c (+.c (*.c (*.c (*.c (*.c (*.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (*.c (*.c (*.c (*.c (*.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1))) (*.c (complex 6 0) (complex -1 1))) (complex 1 0))))