Average Error: 0.0 → 0.0
Time: 25.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r18188 = 0.5;
        double r18189 = re;
        double r18190 = sin(r18189);
        double r18191 = r18188 * r18190;
        double r18192 = 0.0;
        double r18193 = im;
        double r18194 = r18192 - r18193;
        double r18195 = exp(r18194);
        double r18196 = exp(r18193);
        double r18197 = r18195 + r18196;
        double r18198 = r18191 * r18197;
        return r18198;
}
↓
double f(double re, double im) {
        double r18199 = 0.0;
        double r18200 = im;
        double r18201 = r18199 - r18200;
        double r18202 = exp(r18201);
        double r18203 = 0.5;
        double r18204 = re;
        double r18205 = sin(r18204);
        double r18206 = r18203 * r18205;
        double r18207 = r18202 * r18206;
        double r18208 = exp(r18200);
        double r18209 = r18208 * r18206;
        double r18210 = r18207 + r18209;
        return r18210;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))