Average Error: 0.0 → 0.0
Time: 15.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r1710954 = 0.5;
        double r1710955 = re;
        double r1710956 = cos(r1710955);
        double r1710957 = r1710954 * r1710956;
        double r1710958 = im;
        double r1710959 = -r1710958;
        double r1710960 = exp(r1710959);
        double r1710961 = exp(r1710958);
        double r1710962 = r1710960 + r1710961;
        double r1710963 = r1710957 * r1710962;
        return r1710963;
}
↓
double f(double re, double im) {
        double r1710964 = im;
        double r1710965 = exp(r1710964);
        double r1710966 = -r1710964;
        double r1710967 = exp(r1710966);
        double r1710968 = r1710965 + r1710967;
        double r1710969 = 0.5;
        double r1710970 = re;
        double r1710971 = cos(r1710970);
        double r1710972 = r1710969 * r1710971;
        double r1710973 = r1710968 * r1710972;
        return r1710973;
}

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

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))