Average Error: 0.0 → 0.0
Time: 16.7s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\left(0.5 \cdot \sin re\right) \cdot \sqrt{e^{0.0 - im}}\right) \cdot \sqrt{e^{0.0 - im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\left(0.5 \cdot \sin re\right) \cdot \sqrt{e^{0.0 - im}}\right) \cdot \sqrt{e^{0.0 - im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r24089 = 0.5;
        double r24090 = re;
        double r24091 = sin(r24090);
        double r24092 = r24089 * r24091;
        double r24093 = 0.0;
        double r24094 = im;
        double r24095 = r24093 - r24094;
        double r24096 = exp(r24095);
        double r24097 = exp(r24094);
        double r24098 = r24096 + r24097;
        double r24099 = r24092 * r24098;
        return r24099;
}
↓
double f(double re, double im) {
        double r24100 = 0.5;
        double r24101 = re;
        double r24102 = sin(r24101);
        double r24103 = r24100 * r24102;
        double r24104 = 0.0;
        double r24105 = im;
        double r24106 = r24104 - r24105;
        double r24107 = exp(r24106);
        double r24108 = sqrt(r24107);
        double r24109 = r24103 * r24108;
        double r24110 = r24109 * r24108;
        double r24111 = exp(r24105);
        double r24112 = r24103 * r24111;
        double r24113 = r24110 + r24112;
        return r24113;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.0

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

  6. Applied associate-*r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))