Average Error: 45.5 → 44.1
Time: 53.8s
Precision: 64
\[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2.0 + 1.0\right) \cdot z\right) \cdot t}{16.0}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2.0 + 1.0\right) \cdot b\right) \cdot t}{16.0}\right)\]
↓
\[x\]
\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2.0 + 1.0\right) \cdot z\right) \cdot t}{16.0}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2.0 + 1.0\right) \cdot b\right) \cdot t}{16.0}\right)
↓
x
double f(double x, double y, double z, double t, double a, double b) {
        double r44214466 = x;
        double r44214467 = y;
        double r44214468 = 2.0;
        double r44214469 = r44214467 * r44214468;
        double r44214470 = 1.0;
        double r44214471 = r44214469 + r44214470;
        double r44214472 = z;
        double r44214473 = r44214471 * r44214472;
        double r44214474 = t;
        double r44214475 = r44214473 * r44214474;
        double r44214476 = 16.0;
        double r44214477 = r44214475 / r44214476;
        double r44214478 = cos(r44214477);
        double r44214479 = r44214466 * r44214478;
        double r44214480 = a;
        double r44214481 = r44214480 * r44214468;
        double r44214482 = r44214481 + r44214470;
        double r44214483 = b;
        double r44214484 = r44214482 * r44214483;
        double r44214485 = r44214484 * r44214474;
        double r44214486 = r44214485 / r44214476;
        double r44214487 = cos(r44214486);
        double r44214488 = r44214479 * r44214487;
        return r44214488;
}
↓
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 r44214489 = x;
        return r44214489;
}

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

Original45.5
Target44.3
Herbie44.1
\[x \cdot \cos \left(\frac{b}{16.0} \cdot \frac{t}{\left(1.0 - a \cdot 2.0\right) + {\left(a \cdot 2.0\right)}^{2}}\right)\]

Derivation

  1. Initial program 45.5

    \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2.0 + 1.0\right) \cdot z\right) \cdot t}{16.0}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2.0 + 1.0\right) \cdot b\right) \cdot t}{16.0}\right)\]

  2. Taylor expanded around 0 45.0

    \[\leadsto \left(x \cdot \color{blue}{1}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2.0 + 1.0\right) \cdot b\right) \cdot t}{16.0}\right)\]

  3. Taylor expanded around 0 44.1

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

  4. Final simplification44.1

    \[\leadsto x\]

Reproduce

herbie shell --seed 2019158 
(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))))))

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