Average Error: 0.0 → 0.0
Time: 26.0s
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 r16198 = 0.5;
        double r16199 = re;
        double r16200 = sin(r16199);
        double r16201 = r16198 * r16200;
        double r16202 = 0.0;
        double r16203 = im;
        double r16204 = r16202 - r16203;
        double r16205 = exp(r16204);
        double r16206 = exp(r16203);
        double r16207 = r16205 + r16206;
        double r16208 = r16201 * r16207;
        return r16208;
}
↓
double f(double re, double im) {
        double r16209 = 0.0;
        double r16210 = im;
        double r16211 = r16209 - r16210;
        double r16212 = exp(r16211);
        double r16213 = 0.5;
        double r16214 = re;
        double r16215 = sin(r16214);
        double r16216 = r16213 * r16215;
        double r16217 = r16212 * r16216;
        double r16218 = exp(r16210);
        double r16219 = r16218 * r16216;
        double r16220 = r16217 + r16219;
        return r16220;
}

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 2019199 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))