Average Error: 7.3 → 0.2
Time: 12.6s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.re - {x.im}^{3}\]
\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re
↓
\left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.re - {x.im}^{3}
double f(double x_re, double x_im) {
        double r259977 = x_re;
        double r259978 = r259977 * r259977;
        double r259979 = x_im;
        double r259980 = r259979 * r259979;
        double r259981 = r259978 - r259980;
        double r259982 = r259981 * r259979;
        double r259983 = r259977 * r259979;
        double r259984 = r259979 * r259977;
        double r259985 = r259983 + r259984;
        double r259986 = r259985 * r259977;
        double r259987 = r259982 + r259986;
        return r259987;
}
↓
double f(double x_re, double x_im) {
        double r259988 = 3.0;
        double r259989 = x_re;
        double r259990 = x_im;
        double r259991 = r259989 * r259990;
        double r259992 = r259988 * r259991;
        double r259993 = r259992 * r259989;
        double r259994 = pow(r259990, r259988);
        double r259995 = r259993 - r259994;
        return r259995;
}

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

Original7.3
Target0.2
Herbie0.2
\[\left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.3

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

  2. Simplified0.2

    \[\leadsto \color{blue}{3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.re\right) - {x.im}^{3}}\]
  3. Using strategy rm

  4. Applied associate-*r*0.2

    \[\leadsto \color{blue}{\left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.re} - {x.im}^{3}\]

  5. Final simplification0.2

    \[\leadsto \left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.re - {x.im}^{3}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.im) (* 2 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im)))

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