Average Error: 1.9 → 2.6
Time: 12.2s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\left(b \cdot a + y\right) \cdot z + \left(a \cdot t + x\right)\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\left(b \cdot a + y\right) \cdot z + \left(a \cdot t + x\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r507821 = x;
        double r507822 = y;
        double r507823 = z;
        double r507824 = r507822 * r507823;
        double r507825 = r507821 + r507824;
        double r507826 = t;
        double r507827 = a;
        double r507828 = r507826 * r507827;
        double r507829 = r507825 + r507828;
        double r507830 = r507827 * r507823;
        double r507831 = b;
        double r507832 = r507830 * r507831;
        double r507833 = r507829 + r507832;
        return r507833;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r507834 = b;
        double r507835 = a;
        double r507836 = r507834 * r507835;
        double r507837 = y;
        double r507838 = r507836 + r507837;
        double r507839 = z;
        double r507840 = r507838 * r507839;
        double r507841 = t;
        double r507842 = r507835 * r507841;
        double r507843 = x;
        double r507844 = r507842 + r507843;
        double r507845 = r507840 + r507844;
        return r507845;
}

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

Original1.9
Target0.3
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Initial program 1.9

    \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]

  2. Simplified2.6

    \[\leadsto \color{blue}{\left(x + t \cdot a\right) + z \cdot \left(y + b \cdot a\right)}\]

  3. Final simplification2.6

    \[\leadsto \left(b \cdot a + y\right) \cdot z + \left(a \cdot t + x\right)\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"

  :herbie-target
  (if (< z -1.1820553527347888e+19) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))