Average Error: 0.0 → 0.1
Time: 5.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{0.0 - im} + e^{im}\right)}^{3}}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{0.0 - im} + e^{im}\right)}^{3}}
double f(double re, double im) {
        double r18763 = 0.5;
        double r18764 = re;
        double r18765 = sin(r18764);
        double r18766 = r18763 * r18765;
        double r18767 = 0.0;
        double r18768 = im;
        double r18769 = r18767 - r18768;
        double r18770 = exp(r18769);
        double r18771 = exp(r18768);
        double r18772 = r18770 + r18771;
        double r18773 = r18766 * r18772;
        return r18773;
}
↓
double f(double re, double im) {
        double r18774 = 0.5;
        double r18775 = re;
        double r18776 = sin(r18775);
        double r18777 = r18774 * r18776;
        double r18778 = 0.0;
        double r18779 = im;
        double r18780 = r18778 - r18779;
        double r18781 = exp(r18780);
        double r18782 = exp(r18779);
        double r18783 = r18781 + r18782;
        double r18784 = 3.0;
        double r18785 = pow(r18783, r18784);
        double r18786 = cbrt(r18785);
        double r18787 = r18777 * r18786;
        return r18787;
}

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 add-cbrt-cube0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{0.0 - im} + e^{im}\right)}^{3}}\]

Reproduce

herbie shell --seed 2019352 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))