Average Error: 0.0 → 0.0
Time: 11.9s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \]
↓
\[\left(0.5 \cdot e^{im}\right) \cdot \sin re + \sin re \cdot \frac{0.5}{e^{im}} \]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(0.5 \cdot e^{im}\right) \cdot \sin re + \sin re \cdot \frac{0.5}{e^{im}}

(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)) (* (sin re) (/ 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 ((0.5 * exp(im)) * sin(re)) + (sin(re) * (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

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

  3. Applied fma-udef_binary640.0

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

  4. Applied distribute-rgt-in_binary640.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022081 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))