Average Error: 0.0 → 0.9
Time: 22.3s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\left(0.5 \cdot \sqrt{e^{0.0 - im} + e^{im}}\right) \cdot \sin re\right) \cdot \sqrt{e^{0.0 - im} + e^{im}}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\left(0.5 \cdot \sqrt{e^{0.0 - im} + e^{im}}\right) \cdot \sin re\right) \cdot \sqrt{e^{0.0 - im} + e^{im}}
double f(double re, double im) {
        double r25900 = 0.5;
        double r25901 = re;
        double r25902 = sin(r25901);
        double r25903 = r25900 * r25902;
        double r25904 = 0.0;
        double r25905 = im;
        double r25906 = r25904 - r25905;
        double r25907 = exp(r25906);
        double r25908 = exp(r25905);
        double r25909 = r25907 + r25908;
        double r25910 = r25903 * r25909;
        return r25910;
}
↓
double f(double re, double im) {
        double r25911 = 0.5;
        double r25912 = 0.0;
        double r25913 = im;
        double r25914 = r25912 - r25913;
        double r25915 = exp(r25914);
        double r25916 = exp(r25913);
        double r25917 = r25915 + r25916;
        double r25918 = sqrt(r25917);
        double r25919 = r25911 * r25918;
        double r25920 = re;
        double r25921 = sin(r25920);
        double r25922 = r25919 * r25921;
        double r25923 = r25922 * r25918;
        return r25923;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(\sin re \cdot 0.5\right) \cdot \left(e^{0.0 - im} + e^{im}\right)}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt1.3

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

  5. Applied associate-*r*0.9

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

  6. Simplified0.9

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

  7. Final simplification0.9

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

Reproduce

herbie shell --seed 2019179 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))