Average Error: 0.0 → 0.0
Time: 18.8s
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 r1151000 = 0.5;
        double r1151001 = re;
        double r1151002 = sin(r1151001);
        double r1151003 = r1151000 * r1151002;
        double r1151004 = 0.0;
        double r1151005 = im;
        double r1151006 = r1151004 - r1151005;
        double r1151007 = exp(r1151006);
        double r1151008 = exp(r1151005);
        double r1151009 = r1151007 + r1151008;
        double r1151010 = r1151003 * r1151009;
        return r1151010;
}
↓
double f(double re, double im) {
        double r1151011 = im;
        double r1151012 = exp(r1151011);
        double r1151013 = re;
        double r1151014 = sin(r1151013);
        double r1151015 = r1151012 * r1151014;
        double r1151016 = r1151014 / r1151012;
        double r1151017 = r1151015 + r1151016;
        double r1151018 = 0.5;
        double r1151019 = r1151017 * r1151018;
        return r1151019;
}

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

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))