Average Error: 0.0 → 0.0
Time: 5.1s
Precision: binary64
Cost: 19712
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \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 (- 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(-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

Alternatives

Alternative 1
Error0.7
Cost26440
\[\begin{array}{l} \mathbf{if}\;\sin re \leq -0.02764167353437372 \lor \neg \left(\sin re \leq 2.1939149628453636 \cdot 10^{-16}\right):\\ \;\;\;\;\sin re \cdot \left(0.5 \cdot \left(im \cdot im\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left(0.5 \cdot \left(e^{-im} + e^{im}\right)\right)\\ \end{array}\]
Alternative 2
Error0.9
Cost6976
\[\sin re \cdot \left(0.5 \cdot \left(im \cdot im\right) + 1\right)\]
Alternative 3
Error1.2
Cost6464
\[\sin re\]
Alternative 4
Error59.2
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. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))