Average Error: 0.0 → 0.1
Time: 5.1s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{\left(0.5 \cdot \sin re\right) \cdot \left({\left(e^{0 - im}\right)}^{3} + {\left(e^{im}\right)}^{3}\right)}{e^{0 - im} \cdot e^{0 - im} + \left(e^{im} \cdot e^{im} - e^{0 - im} \cdot e^{im}\right)}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\frac{\left(0.5 \cdot \sin re\right) \cdot \left({\left(e^{0 - im}\right)}^{3} + {\left(e^{im}\right)}^{3}\right)}{e^{0 - im} \cdot e^{0 - im} + \left(e^{im} \cdot e^{im} - e^{0 - im} \cdot e^{im}\right)}
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (/
  (* (* 0.5 (sin re)) (+ (pow (exp (- 0.0 im)) 3.0) (pow (exp im) 3.0)))
  (+
   (* (exp (- 0.0 im)) (exp (- 0.0 im)))
   (- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im))))))
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) sin(re)))) * ((double) (((double) pow(((double) exp(((double) (0.0 - im)))), 3.0)) + ((double) pow(((double) exp(im)), 3.0)))))) / ((double) (((double) (((double) exp(((double) (0.0 - im)))) * ((double) exp(((double) (0.0 - im)))))) + ((double) (((double) (((double) exp(im)) * ((double) exp(im)))) - ((double) (((double) exp(((double) (0.0 - im)))) * ((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 0.0

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied flip3-+_binary640.1

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\frac{{\left(e^{0 - im}\right)}^{3} + {\left(e^{im}\right)}^{3}}{e^{0 - im} \cdot e^{0 - im} + \left(e^{im} \cdot e^{im} - e^{0 - im} \cdot e^{im}\right)}}\]

  4. Applied associate-*r/_binary640.1

    \[\leadsto \color{blue}{\frac{\left(0.5 \cdot \sin re\right) \cdot \left({\left(e^{0 - im}\right)}^{3} + {\left(e^{im}\right)}^{3}\right)}{e^{0 - im} \cdot e^{0 - im} + \left(e^{im} \cdot e^{im} - e^{0 - im} \cdot e^{im}\right)}}\]

  5. Final simplification0.1

    \[\leadsto \frac{\left(0.5 \cdot \sin re\right) \cdot \left({\left(e^{0 - im}\right)}^{3} + {\left(e^{im}\right)}^{3}\right)}{e^{0 - im} \cdot e^{0 - im} + \left(e^{im} \cdot e^{im} - e^{0 - im} \cdot e^{im}\right)}\]

Reproduce

herbie shell --seed 2020205 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))