math.sin on complex, real part

Average Error: 0.0 → 0.1

Time: 5.2s

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 f(double re, double im) {
        double r21287 = 0.5;
        double r21288 = re;
        double r21289 = sin(r21288);
        double r21290 = r21287 * r21289;
        double r21291 = 0.0;
        double r21292 = im;
        double r21293 = r21291 - r21292;
        double r21294 = exp(r21293);
        double r21295 = exp(r21292);
        double r21296 = r21294 + r21295;
        double r21297 = r21290 * r21296;
        return r21297;
}

↓

double f(double re, double im) {
        double r21298 = 0.5;
        double r21299 = re;
        double r21300 = sin(r21299);
        double r21301 = r21298 * r21300;
        double r21302 = 0.0;
        double r21303 = im;
        double r21304 = r21302 - r21303;
        double r21305 = exp(r21304);
        double r21306 = r21301 * r21305;
        double r21307 = exp(r21303);
        double r21308 = r21301 * r21307;
        double r21309 = r21306 + r21308;
        return r21309;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.0

   \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
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 2019354 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))