Average Error: 0.1 → 0.1
Time: 5.6s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\sqrt{e^{0.0 - im}} \cdot \left(\sin re \cdot \sqrt{e^{0.0 - im}}\right)\right) + 0.5 \cdot \left(\sin re \cdot e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \left(\sqrt{e^{0.0 - im}} \cdot \left(\sin re \cdot \sqrt{e^{0.0 - im}}\right)\right) + 0.5 \cdot \left(\sin re \cdot e^{im}\right)
double code(double re, double im) {
	return ((double) (((double) (0.5 * ((double) sin(re)))) * ((double) (((double) exp(((double) (0.0 - im)))) + ((double) exp(im))))));
}
↓
double code(double re, double im) {
	return ((double) (((double) (0.5 * ((double) (((double) sqrt(((double) exp(((double) (0.0 - im)))))) * ((double) (((double) sin(re)) * ((double) sqrt(((double) exp(((double) (0.0 - im)))))))))))) + ((double) (0.5 * ((double) (((double) sin(re)) * ((double) exp(im))))))));
}

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 0.1

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

  3. Applied distribute-lft-in0.1

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

  4. Simplified0.1

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

  5. Simplified0.1

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

  7. Applied add-sqr-sqrt0.1

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

  8. Applied associate-*r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020179 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))