Average Error: 20.8 → 17.2
Time: 27.3s
Precision: 64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{a}{b}}{3}\]
\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}{b}}{3}
double f(double x, double y, double z, double t, double a, double b) {
        double r36117389 = 2.0;
        double r36117390 = x;
        double r36117391 = sqrt(r36117390);
        double r36117392 = r36117389 * r36117391;
        double r36117393 = y;
        double r36117394 = z;
        double r36117395 = t;
        double r36117396 = r36117394 * r36117395;
        double r36117397 = 3.0;
        double r36117398 = r36117396 / r36117397;
        double r36117399 = r36117393 - r36117398;
        double r36117400 = cos(r36117399);
        double r36117401 = r36117392 * r36117400;
        double r36117402 = a;
        double r36117403 = b;
        double r36117404 = r36117403 * r36117397;
        double r36117405 = r36117402 / r36117404;
        double r36117406 = r36117401 - r36117405;
        return r36117406;
}
↓
double f(double x, double y, double __attribute__((unused)) z, double __attribute__((unused)) t, double a, double b) {
        double r36117407 = 2.0;
        double r36117408 = x;
        double r36117409 = sqrt(r36117408);
        double r36117410 = r36117407 * r36117409;
        double r36117411 = y;
        double r36117412 = cos(r36117411);
        double r36117413 = r36117410 * r36117412;
        double r36117414 = a;
        double r36117415 = b;
        double r36117416 = r36117414 / r36117415;
        double r36117417 = 3.0;
        double r36117418 = r36117416 / r36117417;
        double r36117419 = r36117413 - r36117418;
        return r36117419;
}

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
Herbie17.2
\[\begin{array}{l} \mathbf{if}\;z \lt -1.379333748723514136852843173740882251575 \cdot 10^{129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.3333333333333333148296162562473909929395}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z \lt 3.516290613555987147199887107423758623887 \cdot 10^{106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333148296162562473909929395}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

  1. Initial program 20.8

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

  3. Applied associate-/r*20.8

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

  5. Applied cos-diff20.5

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

  6. Applied distribute-lft-in20.5

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

  7. Taylor expanded around 0 21.0

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

  8. Taylor expanded around 0 17.2

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

  9. Final simplification17.2

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"

  :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))))