Average Error: 0.0 → 0.0
Time: 25.7s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{\sin re}{e^{im}} \cdot 0.5 + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{\sin re}{e^{im}} \cdot 0.5 + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r14073 = 0.5;
        double r14074 = re;
        double r14075 = sin(r14074);
        double r14076 = r14073 * r14075;
        double r14077 = 0.0;
        double r14078 = im;
        double r14079 = r14077 - r14078;
        double r14080 = exp(r14079);
        double r14081 = exp(r14078);
        double r14082 = r14080 + r14081;
        double r14083 = r14076 * r14082;
        return r14083;
}
↓
double f(double re, double im) {
        double r14084 = re;
        double r14085 = sin(r14084);
        double r14086 = im;
        double r14087 = exp(r14086);
        double r14088 = r14085 / r14087;
        double r14089 = 0.5;
        double r14090 = r14088 * r14089;
        double r14091 = r14089 * r14085;
        double r14092 = r14091 * r14087;
        double r14093 = r14090 + r14092;
        return r14093;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Taylor expanded around inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))