Average Error: 0.0 → 0.1
Time: 4.9s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{0 - im} + e^{im}\right)}^{3}}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{0 - im} + e^{im}\right)}^{3}}
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) cbrt(((double) pow(((double) (((double) exp(((double) (0.0 - im)))) + ((double) exp(im)))), 3.0))))));
}

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 add-cbrt-cube0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020196 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))