Average Error: 0.0 → 0.0
Time: 10.7s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \cos re\right)\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \cos re\right)\right)
double f(double re, double im) {
        double r53069 = 0.5;
        double r53070 = re;
        double r53071 = cos(r53070);
        double r53072 = r53069 * r53071;
        double r53073 = im;
        double r53074 = -r53073;
        double r53075 = exp(r53074);
        double r53076 = exp(r53073);
        double r53077 = r53075 + r53076;
        double r53078 = r53072 * r53077;
        return r53078;
}
↓
double f(double re, double im) {
        double r53079 = 0.5;
        double r53080 = re;
        double r53081 = cos(r53080);
        double r53082 = r53079 * r53081;
        double r53083 = im;
        double r53084 = exp(r53083);
        double r53085 = r53082 / r53084;
        double r53086 = sqrt(r53084);
        double r53087 = r53086 * r53082;
        double r53088 = r53086 * r53087;
        double r53089 = r53085 + r53088;
        return r53089;
}

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. Simplified0.0

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

  7. Applied add-sqr-sqrt0.0

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

  8. Applied associate-*l*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))