Average Error: 0.1 → 0.1
Time: 24.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r1204946 = 0.5;
        double r1204947 = re;
        double r1204948 = sin(r1204947);
        double r1204949 = r1204946 * r1204948;
        double r1204950 = 0.0;
        double r1204951 = im;
        double r1204952 = r1204950 - r1204951;
        double r1204953 = exp(r1204952);
        double r1204954 = exp(r1204951);
        double r1204955 = r1204953 + r1204954;
        double r1204956 = r1204949 * r1204955;
        return r1204956;
}
↓
double f(double re, double im) {
        double r1204957 = im;
        double r1204958 = exp(r1204957);
        double r1204959 = re;
        double r1204960 = sin(r1204959);
        double r1204961 = r1204958 * r1204960;
        double r1204962 = r1204960 / r1204958;
        double r1204963 = r1204961 + r1204962;
        double r1204964 = 0.5;
        double r1204965 = r1204963 * r1204964;
        return r1204965;
}

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 0.1

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

  2. Taylor expanded around inf 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))