Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\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}
double f(double re, double im) {
        double r17188 = 0.5;
        double r17189 = re;
        double r17190 = sin(r17189);
        double r17191 = r17188 * r17190;
        double r17192 = 0.0;
        double r17193 = im;
        double r17194 = r17192 - r17193;
        double r17195 = exp(r17194);
        double r17196 = exp(r17193);
        double r17197 = r17195 + r17196;
        double r17198 = r17191 * r17197;
        return r17198;
}
↓
double f(double re, double im) {
        double r17199 = 0.5;
        double r17200 = re;
        double r17201 = sin(r17200);
        double r17202 = r17199 * r17201;
        double r17203 = 0.0;
        double r17204 = im;
        double r17205 = r17203 - r17204;
        double r17206 = exp(r17205);
        double r17207 = r17202 * r17206;
        double r17208 = exp(r17204);
        double r17209 = r17202 * r17208;
        double r17210 = r17207 + r17209;
        return r17210;
}

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

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

  3. Applied distribute-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020024 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))