Average Error: 0.0 → 0.0
Time: 26.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r15149 = 0.5;
        double r15150 = re;
        double r15151 = sin(r15150);
        double r15152 = r15149 * r15151;
        double r15153 = 0.0;
        double r15154 = im;
        double r15155 = r15153 - r15154;
        double r15156 = exp(r15155);
        double r15157 = exp(r15154);
        double r15158 = r15156 + r15157;
        double r15159 = r15152 * r15158;
        return r15159;
}
↓
double f(double re, double im) {
        double r15160 = 0.5;
        double r15161 = re;
        double r15162 = sin(r15161);
        double r15163 = r15160 * r15162;
        double r15164 = 0.0;
        double r15165 = im;
        double r15166 = r15164 - r15165;
        double r15167 = exp(r15166);
        double r15168 = r15163 * r15167;
        double r15169 = exp(r15165);
        double r15170 = r15163 * r15169;
        double r15171 = r15168 + r15170;
        return r15171;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 +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))))