Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[e^{\frac{1}{2} \cdot re} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
e^{\frac{1}{2} \cdot re} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)
double f(double re, double im) {
        double r28200 = re;
        double r28201 = exp(r28200);
        double r28202 = im;
        double r28203 = sin(r28202);
        double r28204 = r28201 * r28203;
        return r28204;
}
↓
double f(double re, double im) {
        double r28205 = 0.5;
        double r28206 = re;
        double r28207 = r28205 * r28206;
        double r28208 = exp(r28207);
        double r28209 = exp(r28206);
        double r28210 = sqrt(r28209);
        double r28211 = im;
        double r28212 = sin(r28211);
        double r28213 = r28210 * r28212;
        double r28214 = r28208 * r28213;
        return r28214;
}

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

    \[e^{re} \cdot \sin im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)}\]
  5. Using strategy rm

  6. Applied add-exp-log0.0

    \[\leadsto \color{blue}{e^{\log \left(\sqrt{e^{re}}\right)}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\]

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))