3.9.1 real part (p56)

Average Error: 0 → 0

Time: 24.6s

Precision: 64

Math

\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

↓

\[\Re(\left(\left(\left(\left(1 + 0.0 i\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) + \left(1 \cdot 6 + 0.0 \cdot -1\right) i\right)\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right) + \left(1 \cdot -1 + 1 \cdot -1\right) i\right) \cdot \left(\left(\left(-1 \cdot 20 - 1 \cdot 0.0\right) + 15\right) + \left(0.0 + \left(0.0 \cdot -1 + 20 \cdot 1\right)\right) i\right)\right)\right) + \left(\left(\left(\left(15 + 0.0 i\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) + \left(1 \cdot 6 + 0.0 \cdot -1\right) i\right)\right) \cdot \left(\left(\left(1 \cdot -1 + 1 \cdot -1\right) + \left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) - \left(1 \cdot -1 + 1 \cdot -1\right)\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right) + \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right)\right) i\right)\right) + \left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(\left(1 \cdot -1 + 1 \cdot -1\right) + \left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) - \left(1 \cdot -1 + 1 \cdot -1\right)\right)\right) - \left(1 \cdot -1 + 1 \cdot -1\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right) + \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right)\right)\right) + \left(\left(\left(\left(1 \cdot -1 + 1 \cdot -1\right) + \left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) - \left(1 \cdot -1 + 1 \cdot -1\right)\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right) + \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right)\right) i\right)\right)\right))\]

C

double f() {
        double r1050154 = -1.0;
        double r1050155 = 1.0;
        double r1050156 = /* ERROR: no complex support in C */;
        double r1050157 = r1050156 * r1050156;
        double r1050158 = r1050157 * r1050156;
        double r1050159 = r1050158 * r1050156;
        double r1050160 = r1050159 * r1050156;
        double r1050161 = r1050160 * r1050156;
        double r1050162 = 6.0;
        double r1050163 = 0.0;
        double r1050164 = /* ERROR: no complex support in C */;
        double r1050165 = r1050164 * r1050156;
        double r1050166 = r1050165 * r1050156;
        double r1050167 = r1050166 * r1050156;
        double r1050168 = r1050167 * r1050156;
        double r1050169 = r1050168 * r1050156;
        double r1050170 = r1050161 + r1050169;
        double r1050171 = 15.0;
        double r1050172 = /* ERROR: no complex support in C */;
        double r1050173 = r1050172 * r1050156;
        double r1050174 = r1050173 * r1050156;
        double r1050175 = r1050174 * r1050156;
        double r1050176 = r1050175 * r1050156;
        double r1050177 = r1050170 + r1050176;
        double r1050178 = 20.0;
        double r1050179 = /* ERROR: no complex support in C */;
        double r1050180 = r1050179 * r1050156;
        double r1050181 = r1050180 * r1050156;
        double r1050182 = r1050181 * r1050156;
        double r1050183 = r1050177 + r1050182;
        double r1050184 = r1050183 + r1050174;
        double r1050185 = r1050184 + r1050165;
        double r1050186 = /* ERROR: no complex support in C */;
        double r1050187 = r1050185 + r1050186;
        double r1050188 = /* ERROR: no complex support in C */;
        return r1050188;
}

↓

double f() {
        double r1050189 = 1.0;
        double r1050190 = 0.0;
        double r1050191 = /* ERROR: no complex support in C */;
        double r1050192 = -1.0;
        double r1050193 = 6.0;
        double r1050194 = r1050192 * r1050193;
        double r1050195 = r1050189 * r1050190;
        double r1050196 = r1050194 - r1050195;
        double r1050197 = r1050189 * r1050193;
        double r1050198 = r1050190 * r1050192;
        double r1050199 = r1050197 + r1050198;
        double r1050200 = /* ERROR: no complex support in C */;
        double r1050201 = r1050191 + r1050200;
        double r1050202 = r1050189 + r1050192;
        double r1050203 = r1050192 - r1050189;
        double r1050204 = r1050202 * r1050203;
        double r1050205 = r1050189 * r1050192;
        double r1050206 = r1050205 + r1050205;
        double r1050207 = /* ERROR: no complex support in C */;
        double r1050208 = 20.0;
        double r1050209 = r1050192 * r1050208;
        double r1050210 = r1050209 - r1050195;
        double r1050211 = 15.0;
        double r1050212 = r1050210 + r1050211;
        double r1050213 = r1050208 * r1050189;
        double r1050214 = r1050198 + r1050213;
        double r1050215 = r1050190 + r1050214;
        double r1050216 = /* ERROR: no complex support in C */;
        double r1050217 = r1050207 * r1050216;
        double r1050218 = r1050201 + r1050217;
        double r1050219 = /* ERROR: no complex support in C */;
        double r1050220 = r1050219 + r1050200;
        double r1050221 = r1050206 + r1050204;
        double r1050222 = r1050204 - r1050206;
        double r1050223 = r1050221 * r1050222;
        double r1050224 = r1050204 * r1050206;
        double r1050225 = r1050224 + r1050224;
        double r1050226 = /* ERROR: no complex support in C */;
        double r1050227 = r1050220 * r1050226;
        double r1050228 = r1050204 * r1050223;
        double r1050229 = r1050206 * r1050225;
        double r1050230 = r1050228 - r1050229;
        double r1050231 = r1050223 * r1050206;
        double r1050232 = r1050225 * r1050204;
        double r1050233 = r1050231 + r1050232;
        double r1050234 = /* ERROR: no complex support in C */;
        double r1050235 = r1050227 + r1050234;
        double r1050236 = r1050218 + r1050235;
        double r1050237 = /* ERROR: no complex support in C */;
        return r1050237;
}

Derivation

1. Initial program 0

   \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(-1 + 1 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) + \left(\left(\left(\left(\left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(\left(20 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(\left(15 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(\left(6 + 0.0 i\right) \cdot \left(-1 + 1 i\right)\right)\right) + \left(1 + 0.0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Re(\left(\left(\left(\left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) + \left(6 \cdot 1 + 0.0 \cdot -1\right) i\right) + \left(1 + 0.0 i\right)\right) + \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right) + \left(-1 \cdot 1 + -1 \cdot 1\right) i\right) \cdot \left(\left(15 + \left(-1 \cdot 20 - 1 \cdot 0.0\right)\right) + \left(0.0 + \left(1 \cdot 20 + 0.0 \cdot -1\right)\right) i\right)\right)\right) + \left(\left(\left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right) + \left(-1 \cdot 1 + -1 \cdot 1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right) - \left(-1 \cdot 1 + -1 \cdot 1\right)\right) + \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 \cdot 1 + -1 \cdot 1\right) + \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 \cdot 1 + -1 \cdot 1\right)\right) i\right) \cdot \left(\left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) + \left(6 \cdot 1 + 0.0 \cdot -1\right) i\right) + \left(15 + 0.0 i\right)\right)\right) + \left(\left(\left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right) + \left(-1 \cdot 1 + -1 \cdot 1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right) - \left(-1 \cdot 1 + -1 \cdot 1\right)\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) - \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 \cdot 1 + -1 \cdot 1\right) + \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 \cdot 1 + -1 \cdot 1\right)\right) \cdot \left(-1 \cdot 1 + -1 \cdot 1\right)\right) + \left(\left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right) + \left(-1 \cdot 1 + -1 \cdot 1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right) - \left(-1 \cdot 1 + -1 \cdot 1\right)\right)\right) \cdot \left(-1 \cdot 1 + -1 \cdot 1\right) + \left(\left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 \cdot 1 + -1 \cdot 1\right) + \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right) \cdot \left(-1 \cdot 1 + -1 \cdot 1\right)\right) \cdot \left(\left(-1 - 1\right) \cdot \left(1 + -1\right)\right)\right) i\right)\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Re(\left(\left(\left(\left(1 + 0.0 i\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) + \left(1 \cdot 6 + 0.0 \cdot -1\right) i\right)\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right) + \left(1 \cdot -1 + 1 \cdot -1\right) i\right) \cdot \left(\left(\left(-1 \cdot 20 - 1 \cdot 0.0\right) + 15\right) + \left(0.0 + \left(0.0 \cdot -1 + 20 \cdot 1\right)\right) i\right)\right)\right) + \left(\left(\left(\left(15 + 0.0 i\right) + \left(\left(-1 \cdot 6 - 1 \cdot 0.0\right) + \left(1 \cdot 6 + 0.0 \cdot -1\right) i\right)\right) \cdot \left(\left(\left(1 \cdot -1 + 1 \cdot -1\right) + \left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) - \left(1 \cdot -1 + 1 \cdot -1\right)\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right) + \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right)\right) i\right)\right) + \left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(\left(1 \cdot -1 + 1 \cdot -1\right) + \left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) - \left(1 \cdot -1 + 1 \cdot -1\right)\right)\right) - \left(1 \cdot -1 + 1 \cdot -1\right) \cdot \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right) + \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right)\right)\right) + \left(\left(\left(\left(1 \cdot -1 + 1 \cdot -1\right) + \left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) - \left(1 \cdot -1 + 1 \cdot -1\right)\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right) + \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right)\right) i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019169 
(FPCore ()
  :name "3.9.1 real part (p56)"
  (re (+ (+ (+ (+ (+ (+ (* (* (* (* (* (complex -1.0 1.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (* (* (* (* (* (complex 6.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (* (* (complex 15.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (* (complex 20.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (* (complex 15.0 0.0) (complex -1.0 1.0)) (complex -1.0 1.0))) (* (complex 6.0 0.0) (complex -1.0 1.0))) (complex 1.0 0.0))))