Average Error: 0.0 → 0.0
Time: 4.3s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sin re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (* (sin re) (+ (/ 0.5 (exp im)) (* 0.5 (exp im)))))
double code(double re, double im) {
	return (0.5 * sin(re)) * (exp(0.0 - im) + exp(im));
}
↓
double code(double re, double im) {
	return sin(re) * ((0.5 / exp(im)) + (0.5 * 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. Simplified0.0

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

  4. Applied distribute-rgt-in_binary64_280.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Taylor expanded around inf 0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020349 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))