Average Error: 61.9 → 0
Time: 17.7s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\frac{-1}{2} + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{\sqrt{3}}{-1} i\right)\right) + \left(5 + \frac{\sqrt{3}}{\frac{1}{2}} i\right)\right))\]
\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{-1}{2} + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(\frac{-1}{2} + \frac{-\sqrt{3}}{2} i\right) + \left(6 + \frac{\sqrt{3}}{-1} i\right)\right) + \left(5 + \frac{\sqrt{3}}{\frac{1}{2}} i\right)\right))
double f() {
        double r1181108 = 1.0;
        double r1181109 = -r1181108;
        double r1181110 = 2.0;
        double r1181111 = r1181109 / r1181110;
        double r1181112 = 3.0;
        double r1181113 = sqrt(r1181112);
        double r1181114 = r1181113 / r1181110;
        double r1181115 = /* ERROR: no complex support in C */;
        double r1181116 = r1181115 * r1181115;
        double r1181117 = r1181116 * r1181115;
        double r1181118 = r1181117 * r1181115;
        double r1181119 = -r1181110;
        double r1181120 = 0.0;
        double r1181121 = /* ERROR: no complex support in C */;
        double r1181122 = r1181121 * r1181115;
        double r1181123 = r1181122 * r1181115;
        double r1181124 = r1181123 * r1181115;
        double r1181125 = r1181118 + r1181124;
        double r1181126 = 5.0;
        double r1181127 = /* ERROR: no complex support in C */;
        double r1181128 = r1181127 * r1181115;
        double r1181129 = r1181128 * r1181115;
        double r1181130 = r1181125 + r1181129;
        double r1181131 = 4.0;
        double r1181132 = /* ERROR: no complex support in C */;
        double r1181133 = r1181132 * r1181115;
        double r1181134 = r1181130 + r1181133;
        double r1181135 = 7.0;
        double r1181136 = /* ERROR: no complex support in C */;
        double r1181137 = r1181134 + r1181136;
        double r1181138 = /* ERROR: no complex support in C */;
        return r1181138;
}
↓
double f() {
        double r1181139 = -0.5;
        double r1181140 = 3.0;
        double r1181141 = sqrt(r1181140);
        double r1181142 = -r1181141;
        double r1181143 = 2.0;
        double r1181144 = r1181142 / r1181143;
        double r1181145 = /* ERROR: no complex support in C */;
        double r1181146 = 6.0;
        double r1181147 = -1.0;
        double r1181148 = r1181141 / r1181147;
        double r1181149 = /* ERROR: no complex support in C */;
        double r1181150 = r1181145 + r1181149;
        double r1181151 = r1181145 * r1181150;
        double r1181152 = 5.0;
        double r1181153 = 0.5;
        double r1181154 = r1181141 / r1181153;
        double r1181155 = /* ERROR: no complex support in C */;
        double r1181156 = r1181151 + r1181155;
        double r1181157 = /* ERROR: no complex support in C */;
        return r1181157;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019158 +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))))