Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
double f(double re, double im) {
        double r49932 = 0.5;
        double r49933 = re;
        double r49934 = cos(r49933);
        double r49935 = r49932 * r49934;
        double r49936 = im;
        double r49937 = -r49936;
        double r49938 = exp(r49937);
        double r49939 = exp(r49936);
        double r49940 = r49938 + r49939;
        double r49941 = r49935 * r49940;
        return r49941;
}
↓
double f(double re, double im) {
        double r49942 = 0.5;
        double r49943 = re;
        double r49944 = cos(r49943);
        double r49945 = r49942 * r49944;
        double r49946 = im;
        double r49947 = exp(r49946);
        double r49948 = r49945 / r49947;
        double r49949 = r49945 * r49947;
        double r49950 = r49948 + r49949;
        return r49950;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019346 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))