math.sin on complex, real part

Average Error: 0.1 → 0.1

Time: 5.8s

Precision: 64

Math

\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]

↓

\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

C

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((0.0 - im))) + ((0.5 * sin(re)) * exp(im)));
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.1

   \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
2. Using strategy rm

3. Applied distribute-lft-in 0.1

   \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}}\]

4. Final simplification 0.1

   \[\leadsto \left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

Reproduce

herbie shell --seed 2020106 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))