Average Error: 0.0 → 0.0
Time: 7.4s
Precision: binary64
Cost: 26304
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{im} + \frac{0.5 \cdot \sin re}{e^{im}}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{im} + \frac{0.5 \cdot \sin re}{e^{im}}
(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 im)) (/ (* 0.5 (sin re)) (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(im)) + ((0.5 * sin(re)) / 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

Alternatives

Alternative 1
Error31.3
Cost52288
\[\sqrt{\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)} \cdot \sqrt{\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)}\]
Alternative 2
Error0.7
Cost20096
\[\sin re + \sin re \cdot \left(0.5 \cdot \left(im \cdot im\right) + 0.041666666666666664 \cdot {im}^{4}\right)\]
Alternative 3
Error31.4
Cost19904
\[0.5 \cdot \frac{re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
Alternative 4
Error0.0
Cost19712
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]
Alternative 5
Error0.7
Cost13696
\[\sin re \cdot \left(0.5 \cdot \left(im \cdot im\right) + \left(0.041666666666666664 \cdot {im}^{4} + 1\right)\right)\]
Alternative 6
Error31.5
Cost13312
\[re \cdot \left(0.5 \cdot \left(e^{-im} + e^{im}\right)\right)\]
Alternative 7
Error0.8
Cost6976
\[\sin re \cdot \left(0.5 \cdot \left(im \cdot im\right) + 1\right)\]
Alternative 8
Error1.1
Cost6464
\[\sin re\]
Alternative 9
Error59.0
Cost64
\[1\]
Alternative 10
Error61.3
Cost64
\[0\]
Alternative 11
Error59.3
Cost64
\[-1\]

Error

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_7100.0

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

  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. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2021022 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))