Average Error: 45.7 → 43.8
Time: 31.4s
Precision: 64
\[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\]
↓
\[x\]
\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)
↓
x
double f(double x, double y, double z, double t, double a, double b) {
        double r44497856 = x;
        double r44497857 = y;
        double r44497858 = 2.0;
        double r44497859 = r44497857 * r44497858;
        double r44497860 = 1.0;
        double r44497861 = r44497859 + r44497860;
        double r44497862 = z;
        double r44497863 = r44497861 * r44497862;
        double r44497864 = t;
        double r44497865 = r44497863 * r44497864;
        double r44497866 = 16.0;
        double r44497867 = r44497865 / r44497866;
        double r44497868 = cos(r44497867);
        double r44497869 = r44497856 * r44497868;
        double r44497870 = a;
        double r44497871 = r44497870 * r44497858;
        double r44497872 = r44497871 + r44497860;
        double r44497873 = b;
        double r44497874 = r44497872 * r44497873;
        double r44497875 = r44497874 * r44497864;
        double r44497876 = r44497875 / r44497866;
        double r44497877 = cos(r44497876);
        double r44497878 = r44497869 * r44497877;
        return r44497878;
}
↓
double f(double x, double __attribute__((unused)) y, double __attribute__((unused)) z, double __attribute__((unused)) t, double __attribute__((unused)) a, double __attribute__((unused)) b) {
        double r44497879 = x;
        return r44497879;
}

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

Original45.7
Target44.0
Herbie43.8
\[x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right)\]

Derivation

  1. Initial program 45.7

    \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\]

  2. Taylor expanded around 0 45.1

    \[\leadsto \left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \color{blue}{1}\]

  3. Taylor expanded around 0 43.8

    \[\leadsto \color{blue}{x} \cdot 1\]

  4. Final simplification43.8

    \[\leadsto x\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"

  :herbie-target
  (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0))))))

  (* (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0))) (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))