Average Error: 45.9 → 44.4
Time: 51.1s
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 r43343309 = x;
        double r43343310 = y;
        double r43343311 = 2.0;
        double r43343312 = r43343310 * r43343311;
        double r43343313 = 1.0;
        double r43343314 = r43343312 + r43343313;
        double r43343315 = z;
        double r43343316 = r43343314 * r43343315;
        double r43343317 = t;
        double r43343318 = r43343316 * r43343317;
        double r43343319 = 16.0;
        double r43343320 = r43343318 / r43343319;
        double r43343321 = cos(r43343320);
        double r43343322 = r43343309 * r43343321;
        double r43343323 = a;
        double r43343324 = r43343323 * r43343311;
        double r43343325 = r43343324 + r43343313;
        double r43343326 = b;
        double r43343327 = r43343325 * r43343326;
        double r43343328 = r43343327 * r43343317;
        double r43343329 = r43343328 / r43343319;
        double r43343330 = cos(r43343329);
        double r43343331 = r43343322 * r43343330;
        return r43343331;
}
↓
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 r43343332 = x;
        return r43343332;
}

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

Original45.9
Target44.7
Herbie44.4
\[x \cdot \cos \left(\frac{b}{16.0} \cdot \frac{t}{\left(1.0 - a \cdot 2.0\right) + {\left(a \cdot 2.0\right)}^{2}}\right)\]

Derivation

  1. Initial program 45.9

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

  2. Taylor expanded around 0 45.3

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

  3. Taylor expanded around 0 44.4

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

  4. Final simplification44.4

    \[\leadsto x\]

Reproduce

herbie shell --seed 2019164 
(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))))