Average Error: 46.9 → 44.9
Time: 22.2s
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 r720694 = x;
        double r720695 = y;
        double r720696 = 2.0;
        double r720697 = r720695 * r720696;
        double r720698 = 1.0;
        double r720699 = r720697 + r720698;
        double r720700 = z;
        double r720701 = r720699 * r720700;
        double r720702 = t;
        double r720703 = r720701 * r720702;
        double r720704 = 16.0;
        double r720705 = r720703 / r720704;
        double r720706 = cos(r720705);
        double r720707 = r720694 * r720706;
        double r720708 = a;
        double r720709 = r720708 * r720696;
        double r720710 = r720709 + r720698;
        double r720711 = b;
        double r720712 = r720710 * r720711;
        double r720713 = r720712 * r720702;
        double r720714 = r720713 / r720704;
        double r720715 = cos(r720714);
        double r720716 = r720707 * r720715;
        return r720716;
}
↓
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 r720717 = x;
        return r720717;
}

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

Original46.9
Target45.0
Herbie44.9
\[x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right)\]

Derivation

  1. Initial program 46.9

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

  2. Taylor expanded around 0 46.1

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

  3. Taylor expanded around 0 44.9

    \[\leadsto \left(x \cdot 1\right) \cdot \cos \left(\frac{\color{blue}{0}}{16}\right)\]

  4. Final simplification44.9

    \[\leadsto x\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* x (cos (* (/ b 16) (/ t (+ (- 1 (* a 2)) (pow (* a 2) 2))))))

  (* (* x (cos (/ (* (* (+ (* y 2) 1) z) t) 16))) (cos (/ (* (* (+ (* a 2) 1) b) t) 16))))