Average Error: 2.3 → 2.3
Time: 12.9s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\left(t \cdot a + \left(z \cdot y + x\right)\right) + \left(a \cdot z\right) \cdot b\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\left(t \cdot a + \left(z \cdot y + x\right)\right) + \left(a \cdot z\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r30535988 = x;
        double r30535989 = y;
        double r30535990 = z;
        double r30535991 = r30535989 * r30535990;
        double r30535992 = r30535988 + r30535991;
        double r30535993 = t;
        double r30535994 = a;
        double r30535995 = r30535993 * r30535994;
        double r30535996 = r30535992 + r30535995;
        double r30535997 = r30535994 * r30535990;
        double r30535998 = b;
        double r30535999 = r30535997 * r30535998;
        double r30536000 = r30535996 + r30535999;
        return r30536000;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r30536001 = t;
        double r30536002 = a;
        double r30536003 = r30536001 * r30536002;
        double r30536004 = z;
        double r30536005 = y;
        double r30536006 = r30536004 * r30536005;
        double r30536007 = x;
        double r30536008 = r30536006 + r30536007;
        double r30536009 = r30536003 + r30536008;
        double r30536010 = r30536002 * r30536004;
        double r30536011 = b;
        double r30536012 = r30536010 * r30536011;
        double r30536013 = r30536009 + r30536012;
        return r30536013;
}

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

Derivation

  1. Initial program 2.3

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

  2. Final simplification2.3

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

Reproduce

herbie shell --seed 2019174 
(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)))