Average Error: 46.8 → 44.7
Time: 31.0s
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 r44942758 = x;
        double r44942759 = y;
        double r44942760 = 2.0;
        double r44942761 = r44942759 * r44942760;
        double r44942762 = 1.0;
        double r44942763 = r44942761 + r44942762;
        double r44942764 = z;
        double r44942765 = r44942763 * r44942764;
        double r44942766 = t;
        double r44942767 = r44942765 * r44942766;
        double r44942768 = 16.0;
        double r44942769 = r44942767 / r44942768;
        double r44942770 = cos(r44942769);
        double r44942771 = r44942758 * r44942770;
        double r44942772 = a;
        double r44942773 = r44942772 * r44942760;
        double r44942774 = r44942773 + r44942762;
        double r44942775 = b;
        double r44942776 = r44942774 * r44942775;
        double r44942777 = r44942776 * r44942766;
        double r44942778 = r44942777 / r44942768;
        double r44942779 = cos(r44942778);
        double r44942780 = r44942771 * r44942779;
        return r44942780;
}
↓
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 r44942781 = x;
        return r44942781;
}

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

Original46.8
Target45.0
Herbie44.7
\[x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right)\]

Derivation

  1. Initial program 46.8

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

  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 44.7

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

  4. Final simplification44.7

    \[\leadsto x\]

Reproduce

herbie shell --seed 2019171 
(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))))