Average Error: 0.0 → 0.1
Time: 5.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{\left(0.5 \cdot \sin re\right) \cdot \left({\left(e^{0.0 - im}\right)}^{3} + {\left(e^{im}\right)}^{3}\right)}{e^{0.0 - im} \cdot e^{0.0 - im} + \left(e^{im} \cdot e^{im} - e^{0.0 - im} \cdot e^{im}\right)}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{\left(0.5 \cdot \sin re\right) \cdot \left({\left(e^{0.0 - im}\right)}^{3} + {\left(e^{im}\right)}^{3}\right)}{e^{0.0 - im} \cdot e^{0.0 - im} + \left(e^{im} \cdot e^{im} - e^{0.0 - im} \cdot e^{im}\right)}
double code(double re, double im) {
	return ((0.5 * sin(re)) * (exp((0.0 - im)) + exp(im)));
}
↓
double code(double re, double im) {
	return (((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)))));
}

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 flip3-+0.1

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

  4. Applied associate-*r/0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020102 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))