Average Error: 7.0 → 0.2
Time: 2.9s
Precision: binary64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} + \left(x.re \cdot x.im\right) \cdot \left(x.im \cdot -3\right)\]
\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
↓
{x.re}^{3} + \left(x.re \cdot x.im\right) \cdot \left(x.im \cdot -3\right)
(FPCore (x.re x.im)
 :precision binary64
 (-
  (* (- (* x.re x.re) (* x.im x.im)) x.re)
  (* (+ (* x.re x.im) (* x.im x.re)) x.im)))
↓
(FPCore (x.re x.im)
 :precision binary64
 (+ (pow x.re 3.0) (* (* x.re x.im) (* x.im -3.0))))
double code(double x_46_re, double x_46_im) {
	return ((double) (((double) (((double) (((double) (x_46_re * x_46_re)) - ((double) (x_46_im * x_46_im)))) * x_46_re)) - ((double) (((double) (((double) (x_46_re * x_46_im)) + ((double) (x_46_im * x_46_re)))) * x_46_im))));
}
↓
double code(double x_46_re, double x_46_im) {
	return ((double) (((double) pow(x_46_re, 3.0)) + ((double) (((double) (x_46_re * x_46_im)) * ((double) (x_46_im * -3.0))))));
}

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

Original7.0
Target0.3
Herbie0.2
\[\left(x.re \cdot x.re\right) \cdot \left(x.re - x.im\right) + \left(x.re \cdot x.im\right) \cdot \left(x.re - 3 \cdot x.im\right)\]

Derivation

  1. Initial program Error: 7.0 bits

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

  2. SimplifiedError: 7.0 bits

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

  4. Applied associate-*r*Error: 0.2 bits

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

  5. Final simplificationError: 0.2 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3.0 x.im))))

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