Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r27140 = 0.5;
        double r27141 = re;
        double r27142 = cos(r27141);
        double r27143 = r27140 * r27142;
        double r27144 = im;
        double r27145 = -r27144;
        double r27146 = exp(r27145);
        double r27147 = exp(r27144);
        double r27148 = r27146 + r27147;
        double r27149 = r27143 * r27148;
        return r27149;
}
↓
double f(double re, double im) {
        double r27150 = 0.5;
        double r27151 = re;
        double r27152 = cos(r27151);
        double r27153 = r27150 * r27152;
        double r27154 = im;
        double r27155 = -r27154;
        double r27156 = exp(r27155);
        double r27157 = exp(r27154);
        double r27158 = r27156 + r27157;
        double r27159 = r27153 * r27158;
        return r27159;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]

  2. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))