Average Error: 7.4 → 0.3
Time: 1.0m
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.im\right) \cdot \left(x.im + x.re\right) + x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)\]
\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(\left(x.re - x.im\right) \cdot x.im\right) \cdot \left(x.im + x.re\right) + x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)
double f(double x_re, double x_im) {
        double r6247546 = x_re;
        double r6247547 = r6247546 * r6247546;
        double r6247548 = x_im;
        double r6247549 = r6247548 * r6247548;
        double r6247550 = r6247547 - r6247549;
        double r6247551 = r6247550 * r6247548;
        double r6247552 = r6247546 * r6247548;
        double r6247553 = r6247548 * r6247546;
        double r6247554 = r6247552 + r6247553;
        double r6247555 = r6247554 * r6247546;
        double r6247556 = r6247551 + r6247555;
        return r6247556;
}
↓
double f(double x_re, double x_im) {
        double r6247557 = x_re;
        double r6247558 = x_im;
        double r6247559 = r6247557 - r6247558;
        double r6247560 = r6247559 * r6247558;
        double r6247561 = r6247558 + r6247557;
        double r6247562 = r6247560 * r6247561;
        double r6247563 = r6247557 * r6247558;
        double r6247564 = r6247563 + r6247563;
        double r6247565 = r6247557 * r6247564;
        double r6247566 = r6247562 + r6247565;
        return r6247566;
}

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

Original7.4
Target0.3
Herbie0.3
\[\left(x.re \cdot x.im\right) \cdot \left(2.0 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.4

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

  3. Applied difference-of-squares7.4

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

  4. Applied associate-*l*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"

  :herbie-target
  (+ (* (* x.re x.im) (* 2.0 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)))