Average Error: 20.7 → 17.1
Time: 10.5s
Precision: 64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot 1 + 0\right) - \frac{\frac{a}{b}}{3}\]
\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}
↓
\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot 1 + 0\right) - \frac{\frac{a}{b}}{3}
double f(double x, double y, double z, double t, double a, double b) {
        double r699000 = 2.0;
        double r699001 = x;
        double r699002 = sqrt(r699001);
        double r699003 = r699000 * r699002;
        double r699004 = y;
        double r699005 = z;
        double r699006 = t;
        double r699007 = r699005 * r699006;
        double r699008 = 3.0;
        double r699009 = r699007 / r699008;
        double r699010 = r699004 - r699009;
        double r699011 = cos(r699010);
        double r699012 = r699003 * r699011;
        double r699013 = a;
        double r699014 = b;
        double r699015 = r699014 * r699008;
        double r699016 = r699013 / r699015;
        double r699017 = r699012 - r699016;
        return r699017;
}
↓
double f(double x, double y, double __attribute__((unused)) z, double __attribute__((unused)) t, double a, double b) {
        double r699018 = 2.0;
        double r699019 = x;
        double r699020 = sqrt(r699019);
        double r699021 = r699018 * r699020;
        double r699022 = y;
        double r699023 = cos(r699022);
        double r699024 = 1.0;
        double r699025 = r699023 * r699024;
        double r699026 = 0.0;
        double r699027 = r699025 + r699026;
        double r699028 = r699021 * r699027;
        double r699029 = a;
        double r699030 = b;
        double r699031 = r699029 / r699030;
        double r699032 = 3.0;
        double r699033 = r699031 / r699032;
        double r699034 = r699028 - r699033;
        return r699034;
}

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

Original20.7
Target18.6
Herbie17.1
\[\begin{array}{l} \mathbf{if}\;z \lt -1.379333748723514 \cdot 10^{129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.333333333333333315}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z \lt 3.51629061355598715 \cdot 10^{106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.333333333333333315}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

  1. Initial program 20.7

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

  3. Applied cos-diff20.2

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

  4. Taylor expanded around 0 20.9

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

  5. Taylor expanded around 0 17.1

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

  7. Applied associate-/r*17.1

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

  8. Final simplification17.1

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

Reproduce

herbie shell --seed 2020049 
(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))))