Average Error: 61.9 → 0
Time: 22.1s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\frac{11}{2} + \left(\frac{\sqrt{3}}{-2} + \left(-\sqrt{3}\right)\right) i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{-2} i\right) + \left(5 + \sqrt{3} \cdot 2 i\right)\right))\]
\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(\frac{\sqrt{3}}{-2} + \left(-\sqrt{3}\right)\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 r401067 = 1.0;
        double r401068 = -r401067;
        double r401069 = 2.0;
        double r401070 = r401068 / r401069;
        double r401071 = 3.0;
        double r401072 = sqrt(r401071);
        double r401073 = r401072 / r401069;
        double r401074 = /* ERROR: no complex support in C */;
        double r401075 = r401074 * r401074;
        double r401076 = r401075 * r401074;
        double r401077 = r401076 * r401074;
        double r401078 = -r401069;
        double r401079 = 0.0;
        double r401080 = /* ERROR: no complex support in C */;
        double r401081 = r401080 * r401074;
        double r401082 = r401081 * r401074;
        double r401083 = r401082 * r401074;
        double r401084 = r401077 + r401083;
        double r401085 = 5.0;
        double r401086 = /* ERROR: no complex support in C */;
        double r401087 = r401086 * r401074;
        double r401088 = r401087 * r401074;
        double r401089 = r401084 + r401088;
        double r401090 = 4.0;
        double r401091 = /* ERROR: no complex support in C */;
        double r401092 = r401091 * r401074;
        double r401093 = r401089 + r401092;
        double r401094 = 7.0;
        double r401095 = /* ERROR: no complex support in C */;
        double r401096 = r401093 + r401095;
        double r401097 = /* ERROR: no complex support in C */;
        return r401097;
}
↓
double f() {
        double r401098 = 5.5;
        double r401099 = 3.0;
        double r401100 = sqrt(r401099);
        double r401101 = -2.0;
        double r401102 = r401100 / r401101;
        double r401103 = -r401100;
        double r401104 = r401102 + r401103;
        double r401105 = /* ERROR: no complex support in C */;
        double r401106 = -0.5;
        double r401107 = /* ERROR: no complex support in C */;
        double r401108 = r401105 * r401107;
        double r401109 = 5.0;
        double r401110 = 2.0;
        double r401111 = r401100 * r401110;
        double r401112 = /* ERROR: no complex support in C */;
        double r401113 = r401108 + r401112;
        double r401114 = /* ERROR: no complex support in C */;
        return r401114;
}

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

    \[\leadsto \color{blue}{\Re(\left(\left(5 + 2 \cdot \sqrt{3} i\right) + \left(\left(\left(6 + \left(\frac{1}{4} - \frac{3}{4}\right)\right) + \left(-1 \cdot \sqrt{3} + \frac{\sqrt{3}}{-2}\right) i\right) \cdot \left(\left(\frac{1}{4} - \frac{3}{4}\right) + \frac{\sqrt{3}}{-2} i\right)\right)\right))}\]

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(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))))