Average Error: 0.1 → 0.1
Time: 5.3s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{0.5}{e^{im}} \cdot \sin re + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\frac{0.5}{e^{im}} \cdot \sin re + 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 (exp im)) (sin re)) (* (exp im) (* 0.5 (sin re)))))
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 / exp(im)) * sin(re)) + (exp(im) * (0.5 * 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 0.1

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

  2. Simplified0.1

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

  4. Applied distribute-rgt-in_binary640.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2021173 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))