Average Error: 20.5 → 17.9
Time: 1.3m
Precision: 64
\[\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) - \frac{a}{b \cdot 3.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;y - \frac{t \cdot z}{3.0} = -\infty:\\ \;\;\;\;\left(\sqrt{x} \cdot 2.0\right) \cdot \left(1 + \left(y \cdot \frac{-1}{2}\right) \cdot y\right) - \frac{a}{3.0 \cdot b}\\ \mathbf{elif}\;y - \frac{t \cdot z}{3.0} \le 3.1641114325517214 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(\sin y \cdot \sin \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right)\right) \cdot \left(\sqrt{x} \cdot 2.0\right) + \left(\sqrt{x} \cdot 2.0\right) \cdot \left(\cos y \cdot \log \left(e^{\cos \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3.0 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2.0\right) \cdot \left(1 + \left(y \cdot \frac{-1}{2}\right) \cdot y\right) - \frac{a}{3.0 \cdot b}\\ \end{array}\]
\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}\;y - \frac{t \cdot z}{3.0} = -\infty:\\
\;\;\;\;\left(\sqrt{x} \cdot 2.0\right) \cdot \left(1 + \left(y \cdot \frac{-1}{2}\right) \cdot y\right) - \frac{a}{3.0 \cdot b}\\

\mathbf{elif}\;y - \frac{t \cdot z}{3.0} \le 3.1641114325517214 \cdot 10^{+305}:\\
\;\;\;\;\left(\left(\sin y \cdot \sin \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right)\right) \cdot \left(\sqrt{x} \cdot 2.0\right) + \left(\sqrt{x} \cdot 2.0\right) \cdot \left(\cos y \cdot \log \left(e^{\cos \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3.0 \cdot b}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r37544582 = 2.0;
        double r37544583 = x;
        double r37544584 = sqrt(r37544583);
        double r37544585 = r37544582 * r37544584;
        double r37544586 = y;
        double r37544587 = z;
        double r37544588 = t;
        double r37544589 = r37544587 * r37544588;
        double r37544590 = 3.0;
        double r37544591 = r37544589 / r37544590;
        double r37544592 = r37544586 - r37544591;
        double r37544593 = cos(r37544592);
        double r37544594 = r37544585 * r37544593;
        double r37544595 = a;
        double r37544596 = b;
        double r37544597 = r37544596 * r37544590;
        double r37544598 = r37544595 / r37544597;
        double r37544599 = r37544594 - r37544598;
        return r37544599;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r37544600 = y;
        double r37544601 = t;
        double r37544602 = z;
        double r37544603 = r37544601 * r37544602;
        double r37544604 = 3.0;
        double r37544605 = r37544603 / r37544604;
        double r37544606 = r37544600 - r37544605;
        double r37544607 = -inf.0;
        bool r37544608 = r37544606 <= r37544607;
        double r37544609 = x;
        double r37544610 = sqrt(r37544609);
        double r37544611 = 2.0;
        double r37544612 = r37544610 * r37544611;
        double r37544613 = 1.0;
        double r37544614 = -0.5;
        double r37544615 = r37544600 * r37544614;
        double r37544616 = r37544615 * r37544600;
        double r37544617 = r37544613 + r37544616;
        double r37544618 = r37544612 * r37544617;
        double r37544619 = a;
        double r37544620 = b;
        double r37544621 = r37544604 * r37544620;
        double r37544622 = r37544619 / r37544621;
        double r37544623 = r37544618 - r37544622;
        double r37544624 = 3.1641114325517214e+305;
        bool r37544625 = r37544606 <= r37544624;
        double r37544626 = sin(r37544600);
        double r37544627 = 0.3333333333333333;
        double r37544628 = r37544603 * r37544627;
        double r37544629 = sin(r37544628);
        double r37544630 = r37544626 * r37544629;
        double r37544631 = r37544630 * r37544612;
        double r37544632 = cos(r37544600);
        double r37544633 = cos(r37544628);
        double r37544634 = exp(r37544633);
        double r37544635 = log(r37544634);
        double r37544636 = r37544632 * r37544635;
        double r37544637 = r37544612 * r37544636;
        double r37544638 = r37544631 + r37544637;
        double r37544639 = r37544638 - r37544622;
        double r37544640 = r37544625 ? r37544639 : r37544623;
        double r37544641 = r37544608 ? r37544623 : r37544640;
        return r37544641;
}

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

Original20.5
Target18.6
Herbie17.9
\[\begin{array}{l} \mathbf{if}\;z \lt -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1.0}{y} - \frac{\frac{0.3333333333333333}{z}}{t}\right) - \frac{\frac{a}{3.0}}{b}\\ \mathbf{elif}\;z \lt 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2.0\right) \cdot \cos \left(y - \frac{t}{3.0} \cdot z\right) - \frac{\frac{a}{3.0}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333}{z}}{t}\right) \cdot \left(2.0 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3.0}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- y (/ (* z t) 3.0)) < -inf.0 or 3.1641114325517214e+305 < (- y (/ (* z t) 3.0))

    1. Initial program 63.2

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

    2. Taylor expanded around 0 46.1

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

    3. Simplified46.1

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

    if -inf.0 < (- y (/ (* z t) 3.0)) < 3.1641114325517214e+305

    1. Initial program 14.2

      \[\left(2.0 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3.0}\right) - \frac{a}{b \cdot 3.0}\]
    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. Applied distribute-rgt-in13.8

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

    5. Taylor expanded around inf 13.7

      \[\leadsto \left(\left(\cos y \cdot \color{blue}{\cos \left(0.3333333333333333 \cdot \left(t \cdot z\right)\right)}\right) \cdot \left(2.0 \cdot \sqrt{x}\right) + \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3.0}\right)\right) \cdot \left(2.0 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3.0}\]

    6. Taylor expanded around inf 13.7

      \[\leadsto \left(\left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right) \cdot \left(2.0 \cdot \sqrt{x}\right) + \left(\sin y \cdot \color{blue}{\sin \left(0.3333333333333333 \cdot \left(t \cdot z\right)\right)}\right) \cdot \left(2.0 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3.0}\]
    7. Using strategy rm

    8. Applied add-log-exp13.7

      \[\leadsto \left(\left(\cos y \cdot \color{blue}{\log \left(e^{\cos \left(0.3333333333333333 \cdot \left(t \cdot z\right)\right)}\right)}\right) \cdot \left(2.0 \cdot \sqrt{x}\right) + \left(\sin y \cdot \sin \left(0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right) \cdot \left(2.0 \cdot \sqrt{x}\right)\right) - \frac{a}{b \cdot 3.0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification17.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y - \frac{t \cdot z}{3.0} = -\infty:\\ \;\;\;\;\left(\sqrt{x} \cdot 2.0\right) \cdot \left(1 + \left(y \cdot \frac{-1}{2}\right) \cdot y\right) - \frac{a}{3.0 \cdot b}\\ \mathbf{elif}\;y - \frac{t \cdot z}{3.0} \le 3.1641114325517214 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(\sin y \cdot \sin \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right)\right) \cdot \left(\sqrt{x} \cdot 2.0\right) + \left(\sqrt{x} \cdot 2.0\right) \cdot \left(\cos y \cdot \log \left(e^{\cos \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right)}\right)\right)\right) - \frac{a}{3.0 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2.0\right) \cdot \left(1 + \left(y \cdot \frac{-1}{2}\right) \cdot y\right) - \frac{a}{3.0 \cdot b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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 (- (/ 1.0 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))))