Average Error: 3.6 → 3.7
Time: 11.9s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[x \cdot 2 - \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 27\right) \cdot b\right)\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
x \cdot 2 - \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 27\right) \cdot b\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r502684 = x;
        double r502685 = 2.0;
        double r502686 = r502684 * r502685;
        double r502687 = y;
        double r502688 = 9.0;
        double r502689 = r502687 * r502688;
        double r502690 = z;
        double r502691 = r502689 * r502690;
        double r502692 = t;
        double r502693 = r502691 * r502692;
        double r502694 = r502686 - r502693;
        double r502695 = a;
        double r502696 = 27.0;
        double r502697 = r502695 * r502696;
        double r502698 = b;
        double r502699 = r502697 * r502698;
        double r502700 = r502694 + r502699;
        return r502700;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r502701 = x;
        double r502702 = 2.0;
        double r502703 = r502701 * r502702;
        double r502704 = 9.0;
        double r502705 = y;
        double r502706 = z;
        double r502707 = t;
        double r502708 = r502706 * r502707;
        double r502709 = r502705 * r502708;
        double r502710 = r502704 * r502709;
        double r502711 = a;
        double r502712 = 27.0;
        double r502713 = r502711 * r502712;
        double r502714 = b;
        double r502715 = r502713 * r502714;
        double r502716 = r502710 - r502715;
        double r502717 = r502703 - r502716;
        return r502717;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.6
Target2.6
Herbie3.7
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.0630870322617426e+83 or 5.718628013402842e-49 < t

    1. Initial program 0.8

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*0.8

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)}\]

    4. Simplified0.8

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \color{blue}{\left(b \cdot 27\right)}\]

    if -1.0630870322617426e+83 < t < 5.718628013402842e-49

    1. Initial program 5.5

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied pow15.5

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{{t}^{1}}\right) + \left(a \cdot 27\right) \cdot b\]

    4. Applied pow15.5

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \color{blue}{{z}^{1}}\right) \cdot {t}^{1}\right) + \left(a \cdot 27\right) \cdot b\]

    5. Applied pow15.5

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot \color{blue}{{9}^{1}}\right) \cdot {z}^{1}\right) \cdot {t}^{1}\right) + \left(a \cdot 27\right) \cdot b\]

    6. Applied pow15.5

      \[\leadsto \left(x \cdot 2 - \left(\left(\color{blue}{{y}^{1}} \cdot {9}^{1}\right) \cdot {z}^{1}\right) \cdot {t}^{1}\right) + \left(a \cdot 27\right) \cdot b\]

    7. Applied pow-prod-down5.5

      \[\leadsto \left(x \cdot 2 - \left(\color{blue}{{\left(y \cdot 9\right)}^{1}} \cdot {z}^{1}\right) \cdot {t}^{1}\right) + \left(a \cdot 27\right) \cdot b\]

    8. Applied pow-prod-down5.5

      \[\leadsto \left(x \cdot 2 - \color{blue}{{\left(\left(y \cdot 9\right) \cdot z\right)}^{1}} \cdot {t}^{1}\right) + \left(a \cdot 27\right) \cdot b\]

    9. Applied pow-prod-down5.5

      \[\leadsto \left(x \cdot 2 - \color{blue}{{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)}^{1}}\right) + \left(a \cdot 27\right) \cdot b\]

    10. Simplified0.9

      \[\leadsto \left(x \cdot 2 - {\color{blue}{\left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}}^{1}\right) + \left(a \cdot 27\right) \cdot b\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.7

    \[\leadsto x \cdot 2 - \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 27\right) \cdot b\right)\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b)))

  (+ (- (* x 2) (* (* (* y 9) z) t)) (* (* a 27) b)))