Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-1 \cdot im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{-1 \cdot im} + e^{im}\right)
double f(double re, double im) {
        double r28969 = 0.5;
        double r28970 = re;
        double r28971 = sin(r28970);
        double r28972 = r28969 * r28971;
        double r28973 = 0.0;
        double r28974 = im;
        double r28975 = r28973 - r28974;
        double r28976 = exp(r28975);
        double r28977 = exp(r28974);
        double r28978 = r28976 + r28977;
        double r28979 = r28972 * r28978;
        return r28979;
}
↓
double f(double re, double im) {
        double r28980 = 0.5;
        double r28981 = re;
        double r28982 = sin(r28981);
        double r28983 = r28980 * r28982;
        double r28984 = -1.0;
        double r28985 = im;
        double r28986 = r28984 * r28985;
        double r28987 = exp(r28986);
        double r28988 = exp(r28985);
        double r28989 = r28987 + r28988;
        double r28990 = r28983 * r28989;
        return r28990;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]

  2. Taylor expanded around inf 0.0

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

  3. Simplified0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\left(e^{-1 \cdot im} + e^{im}\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \left(e^{-1 \cdot im} + e^{im}\right)\]

Reproduce

herbie shell --seed 2020039 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))