Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
double f(double re, double im) {
        double r12990 = 0.5;
        double r12991 = re;
        double r12992 = sin(r12991);
        double r12993 = r12990 * r12992;
        double r12994 = 0.0;
        double r12995 = im;
        double r12996 = r12994 - r12995;
        double r12997 = exp(r12996);
        double r12998 = exp(r12995);
        double r12999 = r12997 + r12998;
        double r13000 = r12993 * r12999;
        return r13000;
}
↓
double f(double re, double im) {
        double r13001 = 0.5;
        double r13002 = re;
        double r13003 = sin(r13002);
        double r13004 = r13001 * r13003;
        double r13005 = 0.0;
        double r13006 = im;
        double r13007 = r13005 - r13006;
        double r13008 = exp(r13007);
        double r13009 = exp(r13006);
        double r13010 = r13008 + r13009;
        double r13011 = r13004 * r13010;
        return r13011;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))