Average Error: 20.1 → 17.8
Time: 29.8s
Precision: 64
\[\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) - \frac{a}{b \cdot 3.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) \le 1.9705134585429066 \cdot 10^{+143}:\\ \;\;\;\;\left(\cos y \cdot \left(\left(\sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)} \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3.0}\right)\right) \cdot \left(2.0 \cdot \sqrt{x}\right) - \frac{a}{3.0 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2.0 \cdot \sqrt{x}\right) \cdot \left(\frac{-1}{2} \cdot \left(y \cdot y\right) + 1\right) - \frac{a}{3.0 \cdot b}\\ \end{array}\]
\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) - \frac{a}{b \cdot 3.0}
↓
\begin{array}{l}
\mathbf{if}\;\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) \le 1.9705134585429066 \cdot 10^{+143}:\\
\;\;\;\;\left(\cos y \cdot \left(\left(\sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)} \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3.0}\right)\right) \cdot \left(2.0 \cdot \sqrt{x}\right) - \frac{a}{3.0 \cdot b}\\

\mathbf{else}:\\
\;\;\;\;\left(2.0 \cdot \sqrt{x}\right) \cdot \left(\frac{-1}{2} \cdot \left(y \cdot y\right) + 1\right) - \frac{a}{3.0 \cdot b}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r32644337 = 2.0;
        double r32644338 = x;
        double r32644339 = sqrt(r32644338);
        double r32644340 = r32644337 * r32644339;
        double r32644341 = y;
        double r32644342 = z;
        double r32644343 = t;
        double r32644344 = r32644342 * r32644343;
        double r32644345 = 3.0;
        double r32644346 = r32644344 / r32644345;
        double r32644347 = r32644341 - r32644346;
        double r32644348 = cos(r32644347);
        double r32644349 = r32644340 * r32644348;
        double r32644350 = a;
        double r32644351 = b;
        double r32644352 = r32644351 * r32644345;
        double r32644353 = r32644350 / r32644352;
        double r32644354 = r32644349 - r32644353;
        return r32644354;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r32644355 = 2.0;
        double r32644356 = x;
        double r32644357 = sqrt(r32644356);
        double r32644358 = r32644355 * r32644357;
        double r32644359 = y;
        double r32644360 = z;
        double r32644361 = t;
        double r32644362 = r32644360 * r32644361;
        double r32644363 = 3.0;
        double r32644364 = r32644362 / r32644363;
        double r32644365 = r32644359 - r32644364;
        double r32644366 = cos(r32644365);
        double r32644367 = r32644358 * r32644366;
        double r32644368 = 1.9705134585429066e+143;
        bool r32644369 = r32644367 <= r32644368;
        double r32644370 = cos(r32644359);
        double r32644371 = cos(r32644364);
        double r32644372 = cbrt(r32644371);
        double r32644373 = r32644372 * r32644372;
        double r32644374 = r32644373 * r32644372;
        double r32644375 = r32644370 * r32644374;
        double r32644376 = sin(r32644359);
        double r32644377 = sin(r32644364);
        double r32644378 = r32644376 * r32644377;
        double r32644379 = r32644375 + r32644378;
        double r32644380 = r32644379 * r32644358;
        double r32644381 = a;
        double r32644382 = b;
        double r32644383 = r32644363 * r32644382;
        double r32644384 = r32644381 / r32644383;
        double r32644385 = r32644380 - r32644384;
        double r32644386 = -0.5;
        double r32644387 = r32644359 * r32644359;
        double r32644388 = r32644386 * r32644387;
        double r32644389 = 1.0;
        double r32644390 = r32644388 + r32644389;
        double r32644391 = r32644358 * r32644390;
        double r32644392 = r32644391 - r32644384;
        double r32644393 = r32644369 ? r32644385 : r32644392;
        return r32644393;
}

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

Original20.1
Target18.4
Herbie17.8
\[\begin{array}{l} \mathbf{if}\;z \lt -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.3333333333333333}{z}}{t}\right) - \frac{\frac{a}{3.0}}{b}\\ \mathbf{elif}\;z \lt 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2.0\right) \cdot \cos \left(y - \frac{t}{3.0} \cdot z\right) - \frac{\frac{a}{3.0}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333}{z}}{t}\right) \cdot \left(2.0 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3.0}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) < 1.9705134585429066e+143

    1. Initial program 14.3

      \[\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) - \frac{a}{b \cdot 3.0}\]
    2. Using strategy rm

    3. Applied cos-diff13.8

      \[\leadsto \left(2.0 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3.0}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3.0}\right)\right)} - \frac{a}{b \cdot 3.0}\]
    4. Using strategy rm

    5. Applied add-cube-cbrt13.8

      \[\leadsto \left(2.0 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \color{blue}{\left(\left(\sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)} \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)}\right)} + \sin y \cdot \sin \left(\frac{z \cdot t}{3.0}\right)\right) - \frac{a}{b \cdot 3.0}\]

    if 1.9705134585429066e+143 < (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))

    1. Initial program 54.6

      \[\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) - \frac{a}{b \cdot 3.0}\]

    2. Taylor expanded around 0 42.2

      \[\leadsto \left(2.0 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(1 - \frac{1}{2} \cdot {y}^{2}\right)} - \frac{a}{b \cdot 3.0}\]

    3. Simplified42.2

      \[\leadsto \left(2.0 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\frac{-1}{2} \cdot \left(y \cdot y\right) + 1\right)} - \frac{a}{b \cdot 3.0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification17.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) \le 1.9705134585429066 \cdot 10^{+143}:\\ \;\;\;\;\left(\cos y \cdot \left(\left(\sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)} \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3.0}\right)}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3.0}\right)\right) \cdot \left(2.0 \cdot \sqrt{x}\right) - \frac{a}{3.0 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2.0 \cdot \sqrt{x}\right) \cdot \left(\frac{-1}{2} \cdot \left(y \cdot y\right) + 1\right) - \frac{a}{3.0 \cdot b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"

  :herbie-target
  (if (< z -1.3793337487235141e+129) (- (* (* 2.0 (sqrt x)) (cos (- (/ 1 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3.0) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) (/ (/ a 3.0) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2.0 (sqrt x))) (/ (/ a b) 3.0))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))