3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 17.1s

Precision: 64

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

↓

\[\Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(4 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(\frac{1}{2} + 2\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

C

double f() {
        double r9481 = 1.0;
        double r9482 = -r9481;
        double r9483 = 2.0;
        double r9484 = r9482 / r9483;
        double r9485 = 3.0;
        double r9486 = sqrt(r9485);
        double r9487 = r9486 / r9483;
        double r9488 = /* ERROR: no complex support in C */;
        double r9489 = r9488 * r9488;
        double r9490 = r9489 * r9488;
        double r9491 = r9490 * r9488;
        double r9492 = -r9483;
        double r9493 = 0.0;
        double r9494 = /* ERROR: no complex support in C */;
        double r9495 = r9494 * r9488;
        double r9496 = r9495 * r9488;
        double r9497 = r9496 * r9488;
        double r9498 = r9491 + r9497;
        double r9499 = 5.0;
        double r9500 = /* ERROR: no complex support in C */;
        double r9501 = r9500 * r9488;
        double r9502 = r9501 * r9488;
        double r9503 = r9498 + r9502;
        double r9504 = 4.0;
        double r9505 = /* ERROR: no complex support in C */;
        double r9506 = r9505 * r9488;
        double r9507 = r9503 + r9506;
        double r9508 = 7.0;
        double r9509 = /* ERROR: no complex support in C */;
        double r9510 = r9507 + r9509;
        double r9511 = /* ERROR: no complex support in C */;
        return r9511;
}

↓

double f() {
        double r9512 = 1.0;
        double r9513 = -r9512;
        double r9514 = 2.0;
        double r9515 = r9513 / r9514;
        double r9516 = 3.0;
        double r9517 = sqrt(r9516);
        double r9518 = r9517 / r9514;
        double r9519 = /* ERROR: no complex support in C */;
        double r9520 = 4.0;
        double r9521 = 0.0;
        double r9522 = /* ERROR: no complex support in C */;
        double r9523 = 5.0;
        double r9524 = /* ERROR: no complex support in C */;
        double r9525 = r9512 / r9514;
        double r9526 = r9525 + r9514;
        double r9527 = -r9526;
        double r9528 = r9518 + r9521;
        double r9529 = /* ERROR: no complex support in C */;
        double r9530 = r9519 * r9529;
        double r9531 = r9524 + r9530;
        double r9532 = r9519 * r9531;
        double r9533 = r9522 + r9532;
        double r9534 = r9519 * r9533;
        double r9535 = 7.0;
        double r9536 = /* ERROR: no complex support in C */;
        double r9537 = r9534 + r9536;
        double r9538 = /* ERROR: no complex support in C */;
        return r9538;
}

Derivation

1. Initial program 61.9

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(4 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(\frac{1}{2} + 2\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right)\right)\right) + \left(7 + 0.0 i\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(4 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(\frac{1}{2} + 2\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

Reproduce

herbie shell --seed 2019315 
(FPCore ()
  :name "3.9.2 real part (p56)"
  :precision binary64
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (* (* (* (complex (- 2) 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (* (complex 5 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (* (complex 4 0.0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0.0))))