Average Error: 16.2 → 9.7
Time: 29.7s
Precision: 64
\[\left(\left(\left(\left(-3\right) \cdot x\right) \cdot x + 6 \cdot {y}^{2}\right) \cdot x - 4 \cdot {z}^{3}\right) \cdot x\]
\[\left(\left(\left({\left(\frac{1}{{-1}^{2}}\right)}^{1} \cdot \left(\left(x \cdot y\right) \cdot y\right)\right) \cdot 6 - 3 \cdot {x}^{3}\right) - 4 \cdot {z}^{3}\right) \cdot x\]
\left(\left(\left(\left(-3\right) \cdot x\right) \cdot x + 6 \cdot {y}^{2}\right) \cdot x - 4 \cdot {z}^{3}\right) \cdot x
\left(\left(\left({\left(\frac{1}{{-1}^{2}}\right)}^{1} \cdot \left(\left(x \cdot y\right) \cdot y\right)\right) \cdot 6 - 3 \cdot {x}^{3}\right) - 4 \cdot {z}^{3}\right) \cdot x
double f(double x, double y, double z) {
        double r505313 = 3.0;
        double r505314 = -r505313;
        double r505315 = x;
        double r505316 = r505314 * r505315;
        double r505317 = r505316 * r505315;
        double r505318 = 6.0;
        double r505319 = y;
        double r505320 = 2.0;
        double r505321 = pow(r505319, r505320);
        double r505322 = r505318 * r505321;
        double r505323 = r505317 + r505322;
        double r505324 = r505323 * r505315;
        double r505325 = 4.0;
        double r505326 = z;
        double r505327 = pow(r505326, r505313);
        double r505328 = r505325 * r505327;
        double r505329 = r505324 - r505328;
        double r505330 = r505329 * r505315;
        return r505330;
}

double f(double x, double y, double z) {
        double r505331 = 1.0;
        double r505332 = -1.0;
        double r505333 = 2.0;
        double r505334 = pow(r505332, r505333);
        double r505335 = r505331 / r505334;
        double r505336 = 1.0;
        double r505337 = pow(r505335, r505336);
        double r505338 = x;
        double r505339 = y;
        double r505340 = r505338 * r505339;
        double r505341 = r505340 * r505339;
        double r505342 = r505337 * r505341;
        double r505343 = 6.0;
        double r505344 = r505342 * r505343;
        double r505345 = 3.0;
        double r505346 = 3.0;
        double r505347 = pow(r505338, r505346);
        double r505348 = r505345 * r505347;
        double r505349 = r505344 - r505348;
        double r505350 = 4.0;
        double r505351 = z;
        double r505352 = pow(r505351, r505345);
        double r505353 = r505350 * r505352;
        double r505354 = r505349 - r505353;
        double r505355 = r505354 * r505338;
        return r505355;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.2

    \[\left(\left(\left(\left(-3\right) \cdot x\right) \cdot x + 6 \cdot {y}^{2}\right) \cdot x - 4 \cdot {z}^{3}\right) \cdot x\]
  2. Taylor expanded around -inf 16.1

    \[\leadsto \left(\color{blue}{\left(6 \cdot \left(\left(x \cdot {y}^{2}\right) \cdot {\left(\frac{1}{{-1}^{2}}\right)}^{1}\right) - 3 \cdot {x}^{3}\right)} - 4 \cdot {z}^{3}\right) \cdot x\]
  3. Using strategy rm
  4. Applied sqr-pow16.1

    \[\leadsto \left(\left(6 \cdot \left(\left(x \cdot \color{blue}{\left({y}^{\left(\frac{2}{2}\right)} \cdot {y}^{\left(\frac{2}{2}\right)}\right)}\right) \cdot {\left(\frac{1}{{-1}^{2}}\right)}^{1}\right) - 3 \cdot {x}^{3}\right) - 4 \cdot {z}^{3}\right) \cdot x\]
  5. Applied associate-*r*9.7

    \[\leadsto \left(\left(6 \cdot \left(\color{blue}{\left(\left(x \cdot {y}^{\left(\frac{2}{2}\right)}\right) \cdot {y}^{\left(\frac{2}{2}\right)}\right)} \cdot {\left(\frac{1}{{-1}^{2}}\right)}^{1}\right) - 3 \cdot {x}^{3}\right) - 4 \cdot {z}^{3}\right) \cdot x\]
  6. Simplified9.7

    \[\leadsto \left(\left(6 \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot {y}^{\left(\frac{2}{2}\right)}\right) \cdot {\left(\frac{1}{{-1}^{2}}\right)}^{1}\right) - 3 \cdot {x}^{3}\right) - 4 \cdot {z}^{3}\right) \cdot x\]
  7. Final simplification9.7

    \[\leadsto \left(\left(\left({\left(\frac{1}{{-1}^{2}}\right)}^{1} \cdot \left(\left(x \cdot y\right) \cdot y\right)\right) \cdot 6 - 3 \cdot {x}^{3}\right) - 4 \cdot {z}^{3}\right) \cdot x\]

Reproduce

herbie shell --seed 1 
(FPCore (x y z)
  :name "(((-3*x)*x+6*pow(y,2))*x - 4*pow(z,3))*x "
  :precision binary64
  (* (- (* (+ (* (* (- 3) x) x) (* 6 (pow y 2))) x) (* 4 (pow z 3))) x))