3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 4.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f() {
        double r3425 = 1.0;
        double r3426 = -r3425;
        double r3427 = 2.0;
        double r3428 = r3426 / r3427;
        double r3429 = 3.0;
        double r3430 = sqrt(r3429);
        double r3431 = r3430 / r3427;
        double r3432 = /* ERROR: no complex support in C */;
        double r3433 = r3432 * r3432;
        double r3434 = r3433 * r3432;
        double r3435 = r3434 * r3432;
        double r3436 = -r3427;
        double r3437 = 0.0;
        double r3438 = /* ERROR: no complex support in C */;
        double r3439 = r3438 * r3432;
        double r3440 = r3439 * r3432;
        double r3441 = r3440 * r3432;
        double r3442 = r3435 + r3441;
        double r3443 = 5.0;
        double r3444 = /* ERROR: no complex support in C */;
        double r3445 = r3444 * r3432;
        double r3446 = r3445 * r3432;
        double r3447 = r3442 + r3446;
        double r3448 = 4.0;
        double r3449 = /* ERROR: no complex support in C */;
        double r3450 = r3449 * r3432;
        double r3451 = r3447 + r3450;
        double r3452 = 7.0;
        double r3453 = /* ERROR: no complex support in C */;
        double r3454 = r3451 + r3453;
        double r3455 = /* ERROR: no complex support in C */;
        return r3455;
}

↓

double f() {
        double r3456 = 1.0;
        double r3457 = -r3456;
        double r3458 = 2.0;
        double r3459 = r3457 / r3458;
        double r3460 = 3.0;
        double r3461 = sqrt(r3460);
        double r3462 = r3461 / r3458;
        double r3463 = /* ERROR: no complex support in C */;
        double r3464 = 5.0;
        double r3465 = 0.0;
        double r3466 = /* ERROR: no complex support in C */;
        double r3467 = r3459 - r3458;
        double r3468 = r3462 + r3465;
        double r3469 = /* ERROR: no complex support in C */;
        double r3470 = r3469 * r3463;
        double r3471 = r3466 + r3470;
        double r3472 = r3463 * r3471;
        double r3473 = 4.0;
        double r3474 = /* ERROR: no complex support in C */;
        double r3475 = r3472 + r3474;
        double r3476 = r3463 * r3475;
        double r3477 = 7.0;
        double r3478 = /* ERROR: no complex support in C */;
        double r3479 = r3476 + r3478;
        double r3480 = /* ERROR: no complex support in C */;
        return r3480;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2020045 
(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))))