Average Error: 20.8 → 17.9
Time: 11.9s
Precision: binary64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 1.2696895467572062 \cdot 10^{+306}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(1 + y \cdot \left(y \cdot -0.5\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos y \cdot \left(\sqrt{x} \cdot \sqrt[3]{{\left(\cos \left(z \cdot \frac{t}{3}\right)\right)}^{3}}\right) + \sin y \cdot \left(\sqrt[3]{\sqrt{x} \cdot \sin \left(z \cdot \frac{t}{3}\right)} \cdot \left(\sqrt[3]{\sqrt{x} \cdot \sin \left(z \cdot \frac{t}{3}\right)} \cdot \sqrt[3]{\sqrt{x} \cdot \sin \left(z \cdot \frac{t}{3}\right)}\right)\right)\right) - \frac{a}{3 \cdot b}\\ \end{array}\]
\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 \leq -\infty \lor \neg \left(z \cdot t \leq 1.2696895467572062 \cdot 10^{+306}\right):\\
\;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(1 + y \cdot \left(y \cdot -0.5\right)\right)\right) - \frac{a}{3 \cdot b}\\

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

\end{array}
(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))
↓
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* z t) (- INFINITY)) (not (<= (* z t) 1.2696895467572062e+306)))
   (- (* 2.0 (* (sqrt x) (+ 1.0 (* y (* y -0.5))))) (/ a (* 3.0 b)))
   (-
    (*
     2.0
     (+
      (* (cos y) (* (sqrt x) (cbrt (pow (cos (* z (/ t 3.0))) 3.0))))
      (*
       (sin y)
       (*
        (cbrt (* (sqrt x) (sin (* z (/ t 3.0)))))
        (*
         (cbrt (* (sqrt x) (sin (* z (/ t 3.0)))))
         (cbrt (* (sqrt x) (sin (* z (/ t 3.0))))))))))
    (/ a (* 3.0 b)))))
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (2.0 * ((double) sqrt(x)))) * ((double) cos(((double) (y - (((double) (z * t)) / 3.0))))))) - (a / ((double) (b * 3.0)))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if (((((double) (z * t)) <= ((double) -(((double) INFINITY)))) || !(((double) (z * t)) <= 1.2696895467572062e+306))) {
		VAR = ((double) (((double) (2.0 * ((double) (((double) sqrt(x)) * ((double) (1.0 + ((double) (y * ((double) (y * -0.5)))))))))) - (a / ((double) (3.0 * b)))));
	} else {
		VAR = ((double) (((double) (2.0 * ((double) (((double) (((double) cos(y)) * ((double) (((double) sqrt(x)) * ((double) cbrt(((double) pow(((double) cos(((double) (z * (t / 3.0))))), 3.0)))))))) + ((double) (((double) sin(y)) * ((double) (((double) cbrt(((double) (((double) sqrt(x)) * ((double) sin(((double) (z * (t / 3.0))))))))) * ((double) (((double) cbrt(((double) (((double) sqrt(x)) * ((double) sin(((double) (z * (t / 3.0))))))))) * ((double) cbrt(((double) (((double) sqrt(x)) * ((double) sin(((double) (z * (t / 3.0))))))))))))))))))) - (a / ((double) (3.0 * b)))));
	}
	return VAR;
}

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

Original20.8
Target18.7
Herbie17.9
\[\begin{array}{l} \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.3333333333333333}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < -inf.0 or 1.26968954675720621e306 < (* z t)

    1. Initial program 63.8

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

    2. Simplified63.8

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

    3. Taylor expanded around 0 45.1

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \color{blue}{\left(1 - 0.5 \cdot {y}^{2}\right)}\right) - \frac{a}{3 \cdot b}\]

    4. Simplified45.1

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \color{blue}{\left(1 + y \cdot \left(y \cdot -0.5\right)\right)}\right) - \frac{a}{3 \cdot b}\]

    if -inf.0 < (* z t) < 1.26968954675720621e306

    1. Initial program 14.4

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

    2. Simplified14.4

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

    4. Applied cos-diff13.9

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

    5. Applied distribute-lft-in13.9

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

    6. Simplified13.9

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

    7. Simplified13.9

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

    9. Applied add-cube-cbrt13.9

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

    11. Applied add-cbrt-cube13.9

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

    12. Simplified13.9

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

  4. Final simplification17.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 1.2696895467572062 \cdot 10^{+306}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(1 + y \cdot \left(y \cdot -0.5\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos y \cdot \left(\sqrt{x} \cdot \sqrt[3]{{\left(\cos \left(z \cdot \frac{t}{3}\right)\right)}^{3}}\right) + \sin y \cdot \left(\sqrt[3]{\sqrt{x} \cdot \sin \left(z \cdot \frac{t}{3}\right)} \cdot \left(\sqrt[3]{\sqrt{x} \cdot \sin \left(z \cdot \frac{t}{3}\right)} \cdot \sqrt[3]{\sqrt{x} \cdot \sin \left(z \cdot \frac{t}{3}\right)}\right)\right)\right) - \frac{a}{3 \cdot b}\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.3793337487235141e+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))))