Average Error: 20.6 → 18.2
Time: 20.6s
Precision: 64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t \le -2.134950766792070736054264212885483840549 \cdot 10^{298} \lor \neg \left(z \cdot t \le 2.609088471259102629340660177783840039975 \cdot 10^{231}\right):\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \sqrt[3]{{\left(\cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right)}^{3}}\right) + \left(\sin y \cdot \sin \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3}\\ \end{array}\]
\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t \le -2.134950766792070736054264212885483840549 \cdot 10^{298} \lor \neg \left(z \cdot t \le 2.609088471259102629340660177783840039975 \cdot 10^{231}\right):\\
\;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \sqrt[3]{{\left(\cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right)}^{3}}\right) + \left(\sin y \cdot \sin \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r596276 = 2.0;
        double r596277 = x;
        double r596278 = sqrt(r596277);
        double r596279 = r596276 * r596278;
        double r596280 = y;
        double r596281 = z;
        double r596282 = t;
        double r596283 = r596281 * r596282;
        double r596284 = 3.0;
        double r596285 = r596283 / r596284;
        double r596286 = r596280 - r596285;
        double r596287 = cos(r596286);
        double r596288 = r596279 * r596287;
        double r596289 = a;
        double r596290 = b;
        double r596291 = r596290 * r596284;
        double r596292 = r596289 / r596291;
        double r596293 = r596288 - r596292;
        return r596293;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r596294 = z;
        double r596295 = t;
        double r596296 = r596294 * r596295;
        double r596297 = -2.1349507667920707e+298;
        bool r596298 = r596296 <= r596297;
        double r596299 = 2.6090884712591026e+231;
        bool r596300 = r596296 <= r596299;
        double r596301 = !r596300;
        bool r596302 = r596298 || r596301;
        double r596303 = 2.0;
        double r596304 = x;
        double r596305 = sqrt(r596304);
        double r596306 = r596303 * r596305;
        double r596307 = 1.0;
        double r596308 = 0.5;
        double r596309 = y;
        double r596310 = 2.0;
        double r596311 = pow(r596309, r596310);
        double r596312 = r596308 * r596311;
        double r596313 = r596307 - r596312;
        double r596314 = r596306 * r596313;
        double r596315 = a;
        double r596316 = b;
        double r596317 = 3.0;
        double r596318 = r596316 * r596317;
        double r596319 = r596315 / r596318;
        double r596320 = r596314 - r596319;
        double r596321 = cos(r596309);
        double r596322 = 0.3333333333333333;
        double r596323 = r596295 * r596294;
        double r596324 = r596322 * r596323;
        double r596325 = cos(r596324);
        double r596326 = 3.0;
        double r596327 = pow(r596325, r596326);
        double r596328 = cbrt(r596327);
        double r596329 = r596321 * r596328;
        double r596330 = r596306 * r596329;
        double r596331 = sin(r596309);
        double r596332 = sin(r596324);
        double r596333 = r596331 * r596332;
        double r596334 = r596333 * r596306;
        double r596335 = r596330 + r596334;
        double r596336 = r596335 - r596319;
        double r596337 = r596302 ? r596320 : r596336;
        return r596337;
}

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

Original20.6
Target18.6
Herbie18.2
\[\begin{array}{l} \mathbf{if}\;z \lt -1.379333748723514136852843173740882251575 \cdot 10^{129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.3333333333333333148296162562473909929395}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z \lt 3.516290613555987147199887107423758623887 \cdot 10^{106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333148296162562473909929395}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < -2.1349507667920707e+298 or 2.6090884712591026e+231 < (* z t)

    1. Initial program 56.4

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]

    2. Taylor expanded around 0 44.8

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(1 - \frac{1}{2} \cdot {y}^{2}\right)} - \frac{a}{b \cdot 3}\]

    if -2.1349507667920707e+298 < (* z t) < 2.6090884712591026e+231

    1. Initial program 13.4

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
    2. Using strategy rm

    3. Applied cos-diff12.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3}\]

    4. Applied distribute-lft-in12.9

      \[\leadsto \color{blue}{\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right) + \left(2 \cdot \sqrt{x}\right) \cdot \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{b \cdot 3}\]

    5. Simplified12.9

      \[\leadsto \left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right) + \color{blue}{\left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)}\right) - \frac{a}{b \cdot 3}\]

    6. Taylor expanded around inf 12.9

      \[\leadsto \left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \color{blue}{\cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)}\right) + \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3}\]

    7. Taylor expanded around inf 12.9

      \[\leadsto \left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right) + \left(\sin y \cdot \color{blue}{\sin \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)}\right) \cdot \left(2 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3}\]
    8. Using strategy rm

    9. Applied add-cbrt-cube12.9

      \[\leadsto \left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \color{blue}{\sqrt[3]{\left(\cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right) \cdot \cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right) \cdot \cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)}}\right) + \left(\sin y \cdot \sin \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3}\]

    10. Simplified12.9

      \[\leadsto \left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \sqrt[3]{\color{blue}{{\left(\cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right)}^{3}}}\right) + \left(\sin y \cdot \sin \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification18.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \le -2.134950766792070736054264212885483840549 \cdot 10^{298} \lor \neg \left(z \cdot t \le 2.609088471259102629340660177783840039975 \cdot 10^{231}\right):\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \sqrt[3]{{\left(\cos \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right)}^{3}}\right) + \left(\sin y \cdot \sin \left(0.3333333333333333148296162562473909929395 \cdot \left(t \cdot z\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.379333748723514e129) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 0.333333333333333315 z) t)))) (/ (/ a 3) b)) (if (< z 3.51629061355598715e106) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 0.333333333333333315 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3))))

  (- (* (* 2 (sqrt x)) (cos (- y (/ (* z t) 3)))) (/ a (* b 3))))