Average Error: 7.1 → 0.3
Time: 23.2s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.im + x.re\right) - \left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im\]
\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im
↓
\left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.im + x.re\right) - \left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im
double f(double x_re, double x_im) {
        double r6879214 = x_re;
        double r6879215 = r6879214 * r6879214;
        double r6879216 = x_im;
        double r6879217 = r6879216 * r6879216;
        double r6879218 = r6879215 - r6879217;
        double r6879219 = r6879218 * r6879214;
        double r6879220 = r6879214 * r6879216;
        double r6879221 = r6879216 * r6879214;
        double r6879222 = r6879220 + r6879221;
        double r6879223 = r6879222 * r6879216;
        double r6879224 = r6879219 - r6879223;
        return r6879224;
}
↓
double f(double x_re, double x_im) {
        double r6879225 = x_re;
        double r6879226 = x_im;
        double r6879227 = r6879225 - r6879226;
        double r6879228 = r6879227 * r6879225;
        double r6879229 = r6879226 + r6879225;
        double r6879230 = r6879228 * r6879229;
        double r6879231 = r6879225 * r6879226;
        double r6879232 = r6879231 + r6879231;
        double r6879233 = r6879232 * r6879226;
        double r6879234 = r6879230 - r6879233;
        return r6879234;
}

Error

Bits error versus x.re

Bits error versus x.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.1
Target0.3
Herbie0.3
\[\left(x.re \cdot x.re\right) \cdot \left(x.re - x.im\right) + \left(x.re \cdot x.im\right) \cdot \left(x.re - 3 \cdot x.im\right)\]

Derivation

  1. Initial program 7.1

    \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
  2. Using strategy rm

  3. Applied difference-of-squares7.1

    \[\leadsto \color{blue}{\left(\left(x.re + x.im\right) \cdot \left(x.re - x.im\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]

  4. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x.re + x.im\right) \cdot \left(\left(x.re - x.im\right) \cdot x.re\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]

  5. Final simplification0.3

    \[\leadsto \left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.im + x.re\right) - \left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im\]

Reproduce

herbie shell --seed 2019146 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"

  :herbie-target
  (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3 x.im))))

  (- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im)))