Average Error: 0.0 → 0.0
Time: 14.3s
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 r1373959 = 0.5;
        double r1373960 = re;
        double r1373961 = cos(r1373960);
        double r1373962 = r1373959 * r1373961;
        double r1373963 = im;
        double r1373964 = -r1373963;
        double r1373965 = exp(r1373964);
        double r1373966 = exp(r1373963);
        double r1373967 = r1373965 + r1373966;
        double r1373968 = r1373962 * r1373967;
        return r1373968;
}
↓
double f(double re, double im) {
        double r1373969 = im;
        double r1373970 = exp(r1373969);
        double r1373971 = -r1373969;
        double r1373972 = exp(r1373971);
        double r1373973 = r1373970 + r1373972;
        double r1373974 = 0.5;
        double r1373975 = re;
        double r1373976 = cos(r1373975);
        double r1373977 = r1373974 * r1373976;
        double r1373978 = r1373973 * r1373977;
        return r1373978;
}

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 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))