Average Error: 0.0 → 0.0
Time: 19.2s
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 r18213 = 0.5;
        double r18214 = re;
        double r18215 = sin(r18214);
        double r18216 = r18213 * r18215;
        double r18217 = 0.0;
        double r18218 = im;
        double r18219 = r18217 - r18218;
        double r18220 = exp(r18219);
        double r18221 = exp(r18218);
        double r18222 = r18220 + r18221;
        double r18223 = r18216 * r18222;
        return r18223;
}
↓
double f(double re, double im) {
        double r18224 = 0.0;
        double r18225 = im;
        double r18226 = r18224 - r18225;
        double r18227 = exp(r18226);
        double r18228 = 0.5;
        double r18229 = re;
        double r18230 = sin(r18229);
        double r18231 = r18228 * r18230;
        double r18232 = r18227 * r18231;
        double r18233 = exp(r18225);
        double r18234 = r18233 * r18231;
        double r18235 = r18232 + r18234;
        return r18235;
}

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 2019208 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))