Average Error: 0.0 → 0.1
Time: 10.8s
Precision: binary64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right) \]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{\log \left(e^{-im} + e^{im}\right)} \]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{\log \left(e^{-im} + e^{im}\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 (log (+ (exp (- im)) (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 * sin(re)) * exp(log(exp(-im) + 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. Applied add-exp-log_binary640.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2022082 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))