Average Error: 3.7 → 3.9
Time: 1.4m
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r637242 = x;
        double r637243 = 2.0;
        double r637244 = r637242 * r637243;
        double r637245 = y;
        double r637246 = 9.0;
        double r637247 = r637245 * r637246;
        double r637248 = z;
        double r637249 = r637247 * r637248;
        double r637250 = t;
        double r637251 = r637249 * r637250;
        double r637252 = r637244 - r637251;
        double r637253 = a;
        double r637254 = 27.0;
        double r637255 = r637253 * r637254;
        double r637256 = b;
        double r637257 = r637255 * r637256;
        double r637258 = r637252 + r637257;
        return r637258;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r637259 = x;
        double r637260 = 2.0;
        double r637261 = r637259 * r637260;
        double r637262 = y;
        double r637263 = 9.0;
        double r637264 = r637262 * r637263;
        double r637265 = z;
        double r637266 = t;
        double r637267 = r637265 * r637266;
        double r637268 = r637264 * r637267;
        double r637269 = r637261 - r637268;
        double r637270 = a;
        double r637271 = 27.0;
        double r637272 = r637270 * r637271;
        double r637273 = b;
        double r637274 = r637272 * r637273;
        double r637275 = r637269 + r637274;
        return r637275;
}

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

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

Derivation

  1. Split input into 3 regimes

  2. if (* (* (* y 9.0) z) t) < -1.843683384587346e+298

    1. Initial program 56.6

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

    3. Applied associate-*l*5.5

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

    if -1.843683384587346e+298 < (* (* (* y 9.0) z) t) < 3.3418495860336724e+300

    1. Initial program 0.4

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

    3. Applied sub-neg0.4

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

    4. Applied associate-+l+0.4

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

    5. Simplified0.3

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

    6. Taylor expanded around inf 0.3

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

    if 3.3418495860336724e+300 < (* (* (* y 9.0) z) t)

    1. Initial program 60.8

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

    3. Applied sub-neg60.8

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

    4. Applied associate-+l+60.8

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

    5. Simplified60.8

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

    7. Applied associate-*l*59.7

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

    9. Applied associate-*l*1.2

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

  4. Final simplification3.9

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

Reproduce

herbie shell --seed 2019298 
(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)))