Average Error: 0.0 → 0.0
Time: 14.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[e^{0.0} \cdot \frac{0.5 \cdot \sin re}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
e^{0.0} \cdot \frac{0.5 \cdot \sin re}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r80561 = 0.5;
        double r80562 = re;
        double r80563 = sin(r80562);
        double r80564 = r80561 * r80563;
        double r80565 = 0.0;
        double r80566 = im;
        double r80567 = r80565 - r80566;
        double r80568 = exp(r80567);
        double r80569 = exp(r80566);
        double r80570 = r80568 + r80569;
        double r80571 = r80564 * r80570;
        return r80571;
}
↓
double f(double re, double im) {
        double r80572 = 0.0;
        double r80573 = exp(r80572);
        double r80574 = 0.5;
        double r80575 = re;
        double r80576 = sin(r80575);
        double r80577 = r80574 * r80576;
        double r80578 = im;
        double r80579 = exp(r80578);
        double r80580 = r80577 / r80579;
        double r80581 = r80573 * r80580;
        double r80582 = r80579 * r80577;
        double r80583 = r80581 + r80582;
        return r80583;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied sub-neg0.0

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

  8. Applied exp-sum0.0

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

  9. Applied associate-*l*0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))