Average Error: 0.0 → 0.0
Time: 5.0s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \]
↓
\[\begin{array}{l} t_0 := 0.5 \cdot \sin re\\ \frac{t_0}{e^{im}} + t_0 \cdot e^{im} \end{array} \]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\begin{array}{l}
t_0 := 0.5 \cdot \sin re\\
\frac{t_0}{e^{im}} + t_0 \cdot e^{im}
\end{array}

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* 0.5 (sin re)))) (+ (/ t_0 (exp im)) (* t_0 (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) {
	double t_0 = 0.5 * sin(re);
	return (t_0 / exp(im)) + (t_0 * 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_binary640.0

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

  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2021207 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))