Average Error: 0.0 → 0.0
Time: 12.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\frac{1}{2} \cdot \sin re\right) \cdot \left(e^{im} + e^{0.0 - im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\frac{1}{2} \cdot \sin re\right) \cdot \left(e^{im} + e^{0.0 - im}\right)
double f(double re, double im) {
        double r20169 = 0.5;
        double r20170 = re;
        double r20171 = sin(r20170);
        double r20172 = r20169 * r20171;
        double r20173 = 0.0;
        double r20174 = im;
        double r20175 = r20173 - r20174;
        double r20176 = exp(r20175);
        double r20177 = exp(r20174);
        double r20178 = r20176 + r20177;
        double r20179 = r20172 * r20178;
        return r20179;
}
↓
double f(double re, double im) {
        double r20180 = 1.0;
        double r20181 = 2.0;
        double r20182 = r20180 / r20181;
        double r20183 = re;
        double r20184 = sin(r20183);
        double r20185 = r20182 * r20184;
        double r20186 = im;
        double r20187 = exp(r20186);
        double r20188 = 0.0;
        double r20189 = r20188 - r20186;
        double r20190 = exp(r20189);
        double r20191 = r20187 + r20190;
        double r20192 = r20185 * r20191;
        return r20192;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \sin re\right) \cdot e^{0.0 - im} + \left(\frac{1}{2} \cdot \sin re\right) \cdot e^{im}}\]
  5. Using strategy rm

  6. Applied exp-diff0.0

    \[\leadsto \left(\frac{1}{2} \cdot \sin re\right) \cdot \color{blue}{\frac{e^{0.0}}{e^{im}}} + \left(\frac{1}{2} \cdot \sin re\right) \cdot e^{im}\]

  7. Applied associate-*l/0.0

    \[\leadsto \color{blue}{\frac{1 \cdot \sin re}{2}} \cdot \frac{e^{0.0}}{e^{im}} + \left(\frac{1}{2} \cdot \sin re\right) \cdot e^{im}\]

  8. Applied frac-times0.0

    \[\leadsto \color{blue}{\frac{\left(1 \cdot \sin re\right) \cdot e^{0.0}}{2 \cdot e^{im}}} + \left(\frac{1}{2} \cdot \sin re\right) \cdot e^{im}\]

  9. Final simplification0.0

    \[\leadsto \left(\frac{1}{2} \cdot \sin re\right) \cdot \left(e^{im} + e^{0.0 - im}\right)\]

Reproduce

herbie shell --seed 2019304 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))