Average Error: 61.9 → 0
Time: 15.8s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\left(4 + 0.0 i\right) + \left(\left(\left(5 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(\frac{1}{2} + 2\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))\]
\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) + 0.0 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(\left(4 + 0.0 i\right) + \left(\left(\left(5 + 0.0 i\right) + \left(\left(\left(-\frac{1}{2}\right) + \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) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right)\right) \cdot \left(\left(-\frac{1}{2}\right) + \frac{\sqrt{3}}{2} i\right)\right) + \left(7 + 0.0 i\right)\right))
double f() {
        double r27176 = 1.0;
        double r27177 = -r27176;
        double r27178 = 2.0;
        double r27179 = r27177 / r27178;
        double r27180 = 3.0;
        double r27181 = sqrt(r27180);
        double r27182 = r27181 / r27178;
        double r27183 = /* ERROR: no complex support in C */;
        double r27184 = r27183 * r27183;
        double r27185 = r27184 * r27183;
        double r27186 = r27185 * r27183;
        double r27187 = -r27178;
        double r27188 = 0.0;
        double r27189 = /* ERROR: no complex support in C */;
        double r27190 = r27189 * r27183;
        double r27191 = r27190 * r27183;
        double r27192 = r27191 * r27183;
        double r27193 = r27186 + r27192;
        double r27194 = 5.0;
        double r27195 = /* ERROR: no complex support in C */;
        double r27196 = r27195 * r27183;
        double r27197 = r27196 * r27183;
        double r27198 = r27193 + r27197;
        double r27199 = 4.0;
        double r27200 = /* ERROR: no complex support in C */;
        double r27201 = r27200 * r27183;
        double r27202 = r27198 + r27201;
        double r27203 = 7.0;
        double r27204 = /* ERROR: no complex support in C */;
        double r27205 = r27202 + r27204;
        double r27206 = /* ERROR: no complex support in C */;
        return r27206;
}
↓
double f() {
        double r27207 = 4.0;
        double r27208 = 0.0;
        double r27209 = /* ERROR: no complex support in C */;
        double r27210 = 5.0;
        double r27211 = /* ERROR: no complex support in C */;
        double r27212 = 1.0;
        double r27213 = 2.0;
        double r27214 = r27212 / r27213;
        double r27215 = -r27214;
        double r27216 = 3.0;
        double r27217 = sqrt(r27216);
        double r27218 = r27217 / r27213;
        double r27219 = /* ERROR: no complex support in C */;
        double r27220 = r27214 + r27213;
        double r27221 = -r27220;
        double r27222 = r27218 + r27208;
        double r27223 = /* ERROR: no complex support in C */;
        double r27224 = r27219 * r27223;
        double r27225 = r27211 + r27224;
        double r27226 = r27225 * r27219;
        double r27227 = r27209 + r27226;
        double r27228 = r27227 * r27219;
        double r27229 = 7.0;
        double r27230 = /* ERROR: no complex support in C */;
        double r27231 = r27228 + r27230;
        double r27232 = /* ERROR: no complex support in C */;
        return r27232;
}

Error

Derivation

  1. Initial program 61.9

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (* (* (* (complex (- 2.0) 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (* (complex 5.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (complex 4.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (complex 7.0 0.0))))