Average Error: 45.9 → 44.5
Time: 35.3s
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 r18674054 = x;
        double r18674055 = y;
        double r18674056 = 2.0;
        double r18674057 = r18674055 * r18674056;
        double r18674058 = 1.0;
        double r18674059 = r18674057 + r18674058;
        double r18674060 = z;
        double r18674061 = r18674059 * r18674060;
        double r18674062 = t;
        double r18674063 = r18674061 * r18674062;
        double r18674064 = 16.0;
        double r18674065 = r18674063 / r18674064;
        double r18674066 = cos(r18674065);
        double r18674067 = r18674054 * r18674066;
        double r18674068 = a;
        double r18674069 = r18674068 * r18674056;
        double r18674070 = r18674069 + r18674058;
        double r18674071 = b;
        double r18674072 = r18674070 * r18674071;
        double r18674073 = r18674072 * r18674062;
        double r18674074 = r18674073 / r18674064;
        double r18674075 = cos(r18674074);
        double r18674076 = r18674067 * r18674075;
        return r18674076;
}
↓
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 r18674077 = x;
        return r18674077;
}

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
Target44.6
Herbie44.5
\[x \cdot \cos \left(\frac{b}{16.0} \cdot \frac{t}{\left(1.0 - a \cdot 2.0\right) + {\left(a \cdot 2.0\right)}^{2}}\right)\]

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 45.4

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

  3. Taylor expanded around 0 44.5

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

  4. Final simplification44.5

    \[\leadsto x\]

Reproduce

herbie shell --seed 2019156 
(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))))