Average Error: 46.6 → 44.6
Time: 24.6s
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 r1143594 = x;
        double r1143595 = y;
        double r1143596 = 2.0;
        double r1143597 = r1143595 * r1143596;
        double r1143598 = 1.0;
        double r1143599 = r1143597 + r1143598;
        double r1143600 = z;
        double r1143601 = r1143599 * r1143600;
        double r1143602 = t;
        double r1143603 = r1143601 * r1143602;
        double r1143604 = 16.0;
        double r1143605 = r1143603 / r1143604;
        double r1143606 = cos(r1143605);
        double r1143607 = r1143594 * r1143606;
        double r1143608 = a;
        double r1143609 = r1143608 * r1143596;
        double r1143610 = r1143609 + r1143598;
        double r1143611 = b;
        double r1143612 = r1143610 * r1143611;
        double r1143613 = r1143612 * r1143602;
        double r1143614 = r1143613 / r1143604;
        double r1143615 = cos(r1143614);
        double r1143616 = r1143607 * r1143615;
        return r1143616;
}
↓
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 r1143617 = x;
        return r1143617;
}

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

Original46.6
Target44.9
Herbie44.6
\[x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right)\]

Derivation

  1. Initial program 46.6

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

  2. Taylor expanded around 0 45.8

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

  3. Taylor expanded around 0 44.6

    \[\leadsto \left(x \cdot \color{blue}{1}\right) \cdot 1\]

  4. Final simplification44.6

    \[\leadsto x\]

Reproduce

herbie shell --seed 2019195 
(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))))