Average Error: 20.6 → 17.0
Time: 17.0s
Precision: binary64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\left(\cos y \cdot \left(2 \cdot \sqrt{x}\right) + \sin y \cdot 0\right) - \frac{\frac{a}{b}}{3}\]
\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}
↓
\left(\cos y \cdot \left(2 \cdot \sqrt{x}\right) + \sin y \cdot 0\right) - \frac{\frac{a}{b}}{3}
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) (((double) (z * t)) / 3.0)))))))) - ((double) (a / ((double) (b * 3.0))))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (((double) cos(y)) * ((double) (2.0 * ((double) sqrt(x)))))) + ((double) (((double) sin(y)) * 0.0)))) - ((double) (((double) (a / b)) / 3.0))));
}

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

Original20.6
Target18.5
Herbie17.0
\[\begin{array}{l} \mathbf{if}\;z \lt -1.379333748723514 \cdot 10^{129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.333333333333333315}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z \lt 3.51629061355598715 \cdot 10^{106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.333333333333333315}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

  1. Initial program 20.6

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

  3. Applied cos-diff20.1

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

  4. Applied distribute-lft-in20.1

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

  5. Simplified20.2

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

  6. Simplified20.1

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

  7. Taylor expanded around 0 20.8

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

  8. Taylor expanded around 0 17.0

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

  10. Applied associate-/r*17.0

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

  11. Final simplification17.0

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

Reproduce

herbie shell --seed 2020179 
(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))))