3.9.1 real part (p56)

Average Error: 0 → 0

Time: 24.0s

Precision: 64

Math

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

↓

\[\Re(\left(\left(\left(-1 \cdot 6 - 0.0 \cdot 1\right) + \mathsf{fma}\left(0.0, -1, 6 \cdot 1\right) i\right) + \left(\left(\left(1 + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 15 - \left(1 \cdot -1 + 1 \cdot -1\right) \cdot 0.0\right)\right) + \left(\mathsf{fma}\left(15, 1 \cdot -1 + 1 \cdot -1, 0.0 \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right)\right) + 0.0\right) i\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right) + \left(1 \cdot -1 + 1 \cdot -1\right) i\right) \cdot \left(\left(\left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right) + \left(1 \cdot -1 + 1 \cdot -1\right)\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right) - \left(1 \cdot -1 + 1 \cdot -1\right)\right) + \left(\left(-1 \cdot 6 - 0.0 \cdot 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) - \mathsf{fma}\left(0.0, -1, 6 \cdot 1\right) \cdot \left(1 \cdot -1 + 1 \cdot -1\right)\right)\right) + \left(\left(-1 \cdot 20 - 0.0 \cdot 1\right) + \left(\left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) \cdot 15 - \left(1 \cdot -1 + 1 \cdot -1\right) \cdot 0.0\right)\right)\right) + \left(\left(\left(\left(1 \cdot -1 + 1 \cdot -1\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right) + \left(1 \cdot -1 + 1 \cdot -1\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right)\right) + \mathsf{fma}\left(-1 \cdot 6 - 0.0 \cdot 1, 1 \cdot -1 + 1 \cdot -1, \mathsf{fma}\left(0.0, -1, 6 \cdot 1\right) \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right)\right)\right) + \left(\mathsf{fma}\left(20, 1, 0.0 \cdot -1\right) + \mathsf{fma}\left(15, 1 \cdot -1 + 1 \cdot -1, 0.0 \cdot \left(\left(1 + -1\right) \cdot \left(-1 - 1\right)\right)\right)\right)\right) i\right)\right)\right)\right))\]

C

double f() {
        double r986954 = -1.0;
        double r986955 = 1.0;
        double r986956 = /* ERROR: no complex support in C */;
        double r986957 = r986956 * r986956;
        double r986958 = r986957 * r986956;
        double r986959 = r986958 * r986956;
        double r986960 = r986959 * r986956;
        double r986961 = r986960 * r986956;
        double r986962 = 6.0;
        double r986963 = 0.0;
        double r986964 = /* ERROR: no complex support in C */;
        double r986965 = r986964 * r986956;
        double r986966 = r986965 * r986956;
        double r986967 = r986966 * r986956;
        double r986968 = r986967 * r986956;
        double r986969 = r986968 * r986956;
        double r986970 = r986961 + r986969;
        double r986971 = 15.0;
        double r986972 = /* ERROR: no complex support in C */;
        double r986973 = r986972 * r986956;
        double r986974 = r986973 * r986956;
        double r986975 = r986974 * r986956;
        double r986976 = r986975 * r986956;
        double r986977 = r986970 + r986976;
        double r986978 = 20.0;
        double r986979 = /* ERROR: no complex support in C */;
        double r986980 = r986979 * r986956;
        double r986981 = r986980 * r986956;
        double r986982 = r986981 * r986956;
        double r986983 = r986977 + r986982;
        double r986984 = r986983 + r986974;
        double r986985 = r986984 + r986965;
        double r986986 = /* ERROR: no complex support in C */;
        double r986987 = r986985 + r986986;
        double r986988 = /* ERROR: no complex support in C */;
        return r986988;
}

↓

double f() {
        double r986989 = -1.0;
        double r986990 = 6.0;
        double r986991 = r986989 * r986990;
        double r986992 = 0.0;
        double r986993 = 1.0;
        double r986994 = r986992 * r986993;
        double r986995 = r986991 - r986994;
        double r986996 = r986990 * r986993;
        double r986997 = fma(r986992, r986989, r986996);
        double r986998 = /* ERROR: no complex support in C */;
        double r986999 = r986993 + r986989;
        double r987000 = r986989 - r986993;
        double r987001 = r986999 * r987000;
        double r987002 = 15.0;
        double r987003 = r987001 * r987002;
        double r987004 = r986993 * r986989;
        double r987005 = r987004 + r987004;
        double r987006 = r987005 * r986992;
        double r987007 = r987003 - r987006;
        double r987008 = r986993 + r987007;
        double r987009 = r986992 * r987001;
        double r987010 = fma(r987002, r987005, r987009);
        double r987011 = r987010 + r986992;
        double r987012 = /* ERROR: no complex support in C */;
        double r987013 = /* ERROR: no complex support in C */;
        double r987014 = r987001 + r987005;
        double r987015 = r987001 - r987005;
        double r987016 = r987014 * r987015;
        double r987017 = r986995 * r987001;
        double r987018 = r986997 * r987005;
        double r987019 = r987017 - r987018;
        double r987020 = r987016 + r987019;
        double r987021 = 20.0;
        double r987022 = r986989 * r987021;
        double r987023 = r987022 - r986994;
        double r987024 = r987023 + r987007;
        double r987025 = r987020 + r987024;
        double r987026 = r987005 * r987001;
        double r987027 = r987026 + r987026;
        double r987028 = r986997 * r987001;
        double r987029 = fma(r986995, r987005, r987028);
        double r987030 = r987027 + r987029;
        double r987031 = r986992 * r986989;
        double r987032 = fma(r987021, r986993, r987031);
        double r987033 = r987032 + r987010;
        double r987034 = r987030 + r987033;
        double r987035 = /* ERROR: no complex support in C */;
        double r987036 = r987013 * r987035;
        double r987037 = r987012 + r987036;
        double r987038 = r986998 + r987037;
        double r987039 = /* ERROR: no complex support in C */;
        return r987039;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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))))