Average Error: 0.0 → 0.0
Time: 4.4s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \frac{\sin re}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
0.5 \cdot \frac{\sin re}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\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) (exp im))) (* (exp im) (* 0.5 (sin re)))))
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) exp(im))))) + ((double) (((double) exp(im)) * ((double) (0.5 * ((double) sin(re))))))));
}

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 distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Taylor expanded around inf 0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020198 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))