Average Error: 20.5 → 17.9
Time: 29.1s
Precision: 64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\begin{array}{l} \mathbf{if}\;y - \frac{z \cdot t}{3} = -\infty \lor \neg \left(y - \frac{z \cdot t}{3} \le 3.516666701465602032849647204560993340237 \cdot 10^{304}\right):\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos \left(\frac{t}{\frac{3}{z}}\right) \cdot \cos y + \sin y \cdot \sin \left(\frac{t \cdot z}{3}\right)\right) - \frac{a}{b \cdot 3}\\ \end{array}\]
\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}\;y - \frac{z \cdot t}{3} = -\infty \lor \neg \left(y - \frac{z \cdot t}{3} \le 3.516666701465602032849647204560993340237 \cdot 10^{304}\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(2 \cdot \sqrt{x}\right) \cdot \left(\cos \left(\frac{t}{\frac{3}{z}}\right) \cdot \cos y + \sin y \cdot \sin \left(\frac{t \cdot z}{3}\right)\right) - \frac{a}{b \cdot 3}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r494891 = 2.0;
        double r494892 = x;
        double r494893 = sqrt(r494892);
        double r494894 = r494891 * r494893;
        double r494895 = y;
        double r494896 = z;
        double r494897 = t;
        double r494898 = r494896 * r494897;
        double r494899 = 3.0;
        double r494900 = r494898 / r494899;
        double r494901 = r494895 - r494900;
        double r494902 = cos(r494901);
        double r494903 = r494894 * r494902;
        double r494904 = a;
        double r494905 = b;
        double r494906 = r494905 * r494899;
        double r494907 = r494904 / r494906;
        double r494908 = r494903 - r494907;
        return r494908;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r494909 = y;
        double r494910 = z;
        double r494911 = t;
        double r494912 = r494910 * r494911;
        double r494913 = 3.0;
        double r494914 = r494912 / r494913;
        double r494915 = r494909 - r494914;
        double r494916 = -inf.0;
        bool r494917 = r494915 <= r494916;
        double r494918 = 3.516666701465602e+304;
        bool r494919 = r494915 <= r494918;
        double r494920 = !r494919;
        bool r494921 = r494917 || r494920;
        double r494922 = 2.0;
        double r494923 = x;
        double r494924 = sqrt(r494923);
        double r494925 = r494922 * r494924;
        double r494926 = 1.0;
        double r494927 = 0.5;
        double r494928 = 2.0;
        double r494929 = pow(r494909, r494928);
        double r494930 = r494927 * r494929;
        double r494931 = r494926 - r494930;
        double r494932 = r494925 * r494931;
        double r494933 = a;
        double r494934 = b;
        double r494935 = r494934 * r494913;
        double r494936 = r494933 / r494935;
        double r494937 = r494932 - r494936;
        double r494938 = r494913 / r494910;
        double r494939 = r494911 / r494938;
        double r494940 = cos(r494939);
        double r494941 = cos(r494909);
        double r494942 = r494940 * r494941;
        double r494943 = sin(r494909);
        double r494944 = r494911 * r494910;
        double r494945 = r494944 / r494913;
        double r494946 = sin(r494945);
        double r494947 = r494943 * r494946;
        double r494948 = r494942 + r494947;
        double r494949 = r494925 * r494948;
        double r494950 = r494949 - r494936;
        double r494951 = r494921 ? r494937 : r494950;
        return r494951;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (- y (/ (* z t) 3.0)) < -inf.0 or 3.516666701465602e+304 < (- y (/ (* z t) 3.0))

    1. Initial program 62.6

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

    2. Taylor expanded around 0 45.6

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

    if -inf.0 < (- y (/ (* z t) 3.0)) < 3.516666701465602e+304

    1. Initial program 14.2

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

    3. Applied add-sqr-sqrt14.2

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

    4. Applied times-frac14.2

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

    6. Applied cos-diff13.8

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

    7. Simplified13.7

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

    8. Simplified13.8

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

  4. Final simplification17.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y - \frac{z \cdot t}{3} = -\infty \lor \neg \left(y - \frac{z \cdot t}{3} \le 3.516666701465602032849647204560993340237 \cdot 10^{304}\right):\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos \left(\frac{t}{\frac{3}{z}}\right) \cdot \cos y + \sin y \cdot \sin \left(\frac{t \cdot z}{3}\right)\right) - \frac{a}{b \cdot 3}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.379333748723514e+129) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3))))

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