Average Error: 2.3 → 2.7
Time: 4.5s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r765903 = x;
        double r765904 = y;
        double r765905 = z;
        double r765906 = r765904 * r765905;
        double r765907 = r765903 + r765906;
        double r765908 = t;
        double r765909 = a;
        double r765910 = r765908 * r765909;
        double r765911 = r765907 + r765910;
        double r765912 = r765909 * r765905;
        double r765913 = b;
        double r765914 = r765912 * r765913;
        double r765915 = r765911 + r765914;
        return r765915;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r765916 = y;
        double r765917 = z;
        double r765918 = r765916 * r765917;
        double r765919 = x;
        double r765920 = a;
        double r765921 = t;
        double r765922 = b;
        double r765923 = r765917 * r765922;
        double r765924 = r765921 + r765923;
        double r765925 = r765920 * r765924;
        double r765926 = r765919 + r765925;
        double r765927 = r765918 + r765926;
        return r765927;
}

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

Original2.3
Target0.4
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Initial program 2.3

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

  2. Simplified2.7

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

  3. Final simplification2.7

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

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000) (+ (* 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)))