3.9.2 real part (p56)

Average Error: 61.9 → 0

Time: 17.5s

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 r9194 = 1.0;
        double r9195 = -r9194;
        double r9196 = 2.0;
        double r9197 = r9195 / r9196;
        double r9198 = 3.0;
        double r9199 = sqrt(r9198);
        double r9200 = r9199 / r9196;
        double r9201 = /* ERROR: no complex support in C */;
        double r9202 = r9201 * r9201;
        double r9203 = r9202 * r9201;
        double r9204 = r9203 * r9201;
        double r9205 = -r9196;
        double r9206 = 0.0;
        double r9207 = /* ERROR: no complex support in C */;
        double r9208 = r9207 * r9201;
        double r9209 = r9208 * r9201;
        double r9210 = r9209 * r9201;
        double r9211 = r9204 + r9210;
        double r9212 = 5.0;
        double r9213 = /* ERROR: no complex support in C */;
        double r9214 = r9213 * r9201;
        double r9215 = r9214 * r9201;
        double r9216 = r9211 + r9215;
        double r9217 = 4.0;
        double r9218 = /* ERROR: no complex support in C */;
        double r9219 = r9218 * r9201;
        double r9220 = r9216 + r9219;
        double r9221 = 7.0;
        double r9222 = /* ERROR: no complex support in C */;
        double r9223 = r9220 + r9222;
        double r9224 = /* ERROR: no complex support in C */;
        return r9224;
}

↓

double f() {
        double r9225 = 1.0;
        double r9226 = -r9225;
        double r9227 = 2.0;
        double r9228 = r9226 / r9227;
        double r9229 = 3.0;
        double r9230 = sqrt(r9229);
        double r9231 = r9230 / r9227;
        double r9232 = /* ERROR: no complex support in C */;
        double r9233 = 4.0;
        double r9234 = 0.0;
        double r9235 = /* ERROR: no complex support in C */;
        double r9236 = 5.0;
        double r9237 = /* ERROR: no complex support in C */;
        double r9238 = r9225 / r9227;
        double r9239 = r9238 + r9227;
        double r9240 = -r9239;
        double r9241 = r9231 + r9234;
        double r9242 = /* ERROR: no complex support in C */;
        double r9243 = r9232 * r9242;
        double r9244 = r9237 + r9243;
        double r9245 = r9232 * r9244;
        double r9246 = r9235 + r9245;
        double r9247 = r9232 * r9246;
        double r9248 = 7.0;
        double r9249 = /* ERROR: no complex support in C */;
        double r9250 = r9247 + r9249;
        double r9251 = /* ERROR: no complex support in C */;
        return r9251;
}

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 2019310 
(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))))