Average Error: 46.6 → 44.5
Time: 29.2s
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 r42200111 = x;
        double r42200112 = y;
        double r42200113 = 2.0;
        double r42200114 = r42200112 * r42200113;
        double r42200115 = 1.0;
        double r42200116 = r42200114 + r42200115;
        double r42200117 = z;
        double r42200118 = r42200116 * r42200117;
        double r42200119 = t;
        double r42200120 = r42200118 * r42200119;
        double r42200121 = 16.0;
        double r42200122 = r42200120 / r42200121;
        double r42200123 = cos(r42200122);
        double r42200124 = r42200111 * r42200123;
        double r42200125 = a;
        double r42200126 = r42200125 * r42200113;
        double r42200127 = r42200126 + r42200115;
        double r42200128 = b;
        double r42200129 = r42200127 * r42200128;
        double r42200130 = r42200129 * r42200119;
        double r42200131 = r42200130 / r42200121;
        double r42200132 = cos(r42200131);
        double r42200133 = r42200124 * r42200132;
        return r42200133;
}
↓
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 r42200134 = x;
        return r42200134;
}

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
Target44.7
Herbie44.5
\[x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right)\]

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

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

  3. Taylor expanded around 0 44.5

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

  4. Final simplification44.5

    \[\leadsto x\]

Reproduce

herbie shell --seed 2019192 
(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))))