Average Error: 20.3 → 16.6
Time: 11.0s
Precision: binary64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{a}{3}}{b}\]
\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}
↓
\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{a}{3}}{b}
(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
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ (/ a 3.0) b)))
double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y - ((z * t) / 3.0))) - (a / (b * 3.0));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - ((a / 3.0) / b);
}

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

Original20.3
Target18.3
Herbie16.6
\[\begin{array}{l} \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.3333333333333333}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

  1. Initial program 20.3

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

  2. Taylor expanded around 0 16.6

    \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{0}\right) - \frac{a}{b \cdot 3}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity_binary6416.6

    \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - 0\right) - \frac{\color{blue}{1 \cdot a}}{b \cdot 3}\]

  5. Applied times-frac_binary6416.7

    \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - 0\right) - \color{blue}{\frac{1}{b} \cdot \frac{a}{3}}\]
  6. Using strategy rm

  7. Applied associate-*l/_binary6416.6

    \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - 0\right) - \color{blue}{\frac{1 \cdot \frac{a}{3}}{b}}\]

  8. Simplified16.6

    \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - 0\right) - \frac{\color{blue}{\frac{a}{3}}}{b}\]

  9. Final simplification16.6

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

Reproduce

herbie shell --seed 2020268 
(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))))