Average Error: 20.5 → 18.0
Time: 28.9s
Precision: 64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \le 0.9999972455529012593800075592298526316881:\\ \;\;\;\;\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right) + \left(2 \cdot \sqrt{x}\right) \cdot \log \left(e^{\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)}\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\ \end{array}\]
\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}\;\cos \left(y - \frac{z \cdot t}{3}\right) \le 0.9999972455529012593800075592298526316881:\\
\;\;\;\;\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 \log \left(e^{\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)}\right)\right) - \frac{a}{b \cdot 3}\\

\mathbf{else}:\\
\;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r510950 = 2.0;
        double r510951 = x;
        double r510952 = sqrt(r510951);
        double r510953 = r510950 * r510952;
        double r510954 = y;
        double r510955 = z;
        double r510956 = t;
        double r510957 = r510955 * r510956;
        double r510958 = 3.0;
        double r510959 = r510957 / r510958;
        double r510960 = r510954 - r510959;
        double r510961 = cos(r510960);
        double r510962 = r510953 * r510961;
        double r510963 = a;
        double r510964 = b;
        double r510965 = r510964 * r510958;
        double r510966 = r510963 / r510965;
        double r510967 = r510962 - r510966;
        return r510967;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r510968 = y;
        double r510969 = z;
        double r510970 = t;
        double r510971 = r510969 * r510970;
        double r510972 = 3.0;
        double r510973 = r510971 / r510972;
        double r510974 = r510968 - r510973;
        double r510975 = cos(r510974);
        double r510976 = 0.9999972455529013;
        bool r510977 = r510975 <= r510976;
        double r510978 = 2.0;
        double r510979 = x;
        double r510980 = sqrt(r510979);
        double r510981 = r510978 * r510980;
        double r510982 = cos(r510968);
        double r510983 = cos(r510973);
        double r510984 = r510982 * r510983;
        double r510985 = r510981 * r510984;
        double r510986 = sin(r510968);
        double r510987 = sin(r510973);
        double r510988 = r510986 * r510987;
        double r510989 = exp(r510988);
        double r510990 = log(r510989);
        double r510991 = r510981 * r510990;
        double r510992 = r510985 + r510991;
        double r510993 = a;
        double r510994 = b;
        double r510995 = r510994 * r510972;
        double r510996 = r510993 / r510995;
        double r510997 = r510992 - r510996;
        double r510998 = 1.0;
        double r510999 = 0.5;
        double r511000 = 2.0;
        double r511001 = pow(r510968, r511000);
        double r511002 = r510999 * r511001;
        double r511003 = r510998 - r511002;
        double r511004 = r510981 * r511003;
        double r511005 = r511004 - r510996;
        double r511006 = r510977 ? r510997 : r511005;
        return r511006;
}

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
Target18.8
Herbie18.0
\[\begin{array}{l} \mathbf{if}\;z \lt -1.379333748723514136852843173740882251575 \cdot 10^{129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.3333333333333333148296162562473909929395}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z \lt 3.516290613555987147199887107423758623887 \cdot 10^{106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333148296162562473909929395}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (cos (- y (/ (* z t) 3.0))) < 0.9999972455529013

    1. Initial program 20.1

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

    3. Applied cos-diff19.5

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

    4. Applied distribute-lft-in19.5

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

    6. Applied add-log-exp19.5

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

    if 0.9999972455529013 < (cos (- y (/ (* z t) 3.0)))

    1. Initial program 21.3

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

    2. Taylor expanded around 0 15.4

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

  4. Final simplification18.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \le 0.9999972455529012593800075592298526316881:\\ \;\;\;\;\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right) + \left(2 \cdot \sqrt{x}\right) \cdot \log \left(e^{\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)}\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(1 - \frac{1}{2} \cdot {y}^{2}\right) - \frac{a}{b \cdot 3}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))))