Average Error: 0.0 → 0.0
Time: 20.5s
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 r12119 = 0.5;
        double r12120 = re;
        double r12121 = sin(r12120);
        double r12122 = r12119 * r12121;
        double r12123 = 0.0;
        double r12124 = im;
        double r12125 = r12123 - r12124;
        double r12126 = exp(r12125);
        double r12127 = exp(r12124);
        double r12128 = r12126 + r12127;
        double r12129 = r12122 * r12128;
        return r12129;
}
↓
double f(double re, double im) {
        double r12130 = 0.5;
        double r12131 = re;
        double r12132 = sin(r12131);
        double r12133 = r12130 * r12132;
        double r12134 = 0.0;
        double r12135 = im;
        double r12136 = r12134 - r12135;
        double r12137 = exp(r12136);
        double r12138 = r12133 * r12137;
        double r12139 = exp(r12135);
        double r12140 = r12133 * r12139;
        double r12141 = r12138 + r12140;
        return r12141;
}

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 2019326 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))