Average Error: 7.3 → 0.2
Time: 17.3s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.re\right) - {x.im}^{3}\]
\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
↓
3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.re\right) - {x.im}^{3}
double f(double x_re, double x_im) {
        double r298483 = x_re;
        double r298484 = r298483 * r298483;
        double r298485 = x_im;
        double r298486 = r298485 * r298485;
        double r298487 = r298484 - r298486;
        double r298488 = r298487 * r298485;
        double r298489 = r298483 * r298485;
        double r298490 = r298485 * r298483;
        double r298491 = r298489 + r298490;
        double r298492 = r298491 * r298483;
        double r298493 = r298488 + r298492;
        return r298493;
}
↓
double f(double x_re, double x_im) {
        double r298494 = 3.0;
        double r298495 = x_re;
        double r298496 = x_im;
        double r298497 = r298495 * r298496;
        double r298498 = r298497 * r298495;
        double r298499 = r298494 * r298498;
        double r298500 = pow(r298496, r298494);
        double r298501 = r298499 - r298500;
        return r298501;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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)))