Average Error: 0.0 → 0.0
Time: 16.1s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \frac{0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \frac{0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}
double f(double re, double im) {
        double r40997 = 0.5;
        double r40998 = re;
        double r40999 = cos(r40998);
        double r41000 = r40997 * r40999;
        double r41001 = im;
        double r41002 = -r41001;
        double r41003 = exp(r41002);
        double r41004 = exp(r41001);
        double r41005 = r41003 + r41004;
        double r41006 = r41000 * r41005;
        return r41006;
}
↓
double f(double re, double im) {
        double r41007 = re;
        double r41008 = cos(r41007);
        double r41009 = 0.5;
        double r41010 = im;
        double r41011 = exp(r41010);
        double r41012 = r41009 / r41011;
        double r41013 = r41008 * r41012;
        double r41014 = r41008 * r41009;
        double r41015 = r41014 * r41011;
        double r41016 = r41013 + r41015;
        return r41016;
}

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. Simplified0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))