Average Error: 2.1 → 2.3
Time: 12.9s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -7.562067749692457 \cdot 10^{+208}:\\ \;\;\;\;\left(b \cdot a + y\right) \cdot z + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot y + \left(\left(t + z \cdot b\right) \cdot a + x\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;z \le -7.562067749692457 \cdot 10^{+208}:\\
\;\;\;\;\left(b \cdot a + y\right) \cdot z + t \cdot a\\

\mathbf{else}:\\
\;\;\;\;z \cdot y + \left(\left(t + z \cdot b\right) \cdot a + x\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r32594975 = x;
        double r32594976 = y;
        double r32594977 = z;
        double r32594978 = r32594976 * r32594977;
        double r32594979 = r32594975 + r32594978;
        double r32594980 = t;
        double r32594981 = a;
        double r32594982 = r32594980 * r32594981;
        double r32594983 = r32594979 + r32594982;
        double r32594984 = r32594981 * r32594977;
        double r32594985 = b;
        double r32594986 = r32594984 * r32594985;
        double r32594987 = r32594983 + r32594986;
        return r32594987;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r32594988 = z;
        double r32594989 = -7.562067749692457e+208;
        bool r32594990 = r32594988 <= r32594989;
        double r32594991 = b;
        double r32594992 = a;
        double r32594993 = r32594991 * r32594992;
        double r32594994 = y;
        double r32594995 = r32594993 + r32594994;
        double r32594996 = r32594995 * r32594988;
        double r32594997 = t;
        double r32594998 = r32594997 * r32594992;
        double r32594999 = r32594996 + r32594998;
        double r32595000 = r32594988 * r32594994;
        double r32595001 = r32594988 * r32594991;
        double r32595002 = r32594997 + r32595001;
        double r32595003 = r32595002 * r32594992;
        double r32595004 = x;
        double r32595005 = r32595003 + r32595004;
        double r32595006 = r32595000 + r32595005;
        double r32595007 = r32594990 ? r32594999 : r32595006;
        return r32595007;
}

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

Original2.1
Target0.4
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.562067749692457e+208

    1. Initial program 10.6

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

    2. Simplified14.4

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

    3. Taylor expanded around inf 24.7

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

    4. Simplified12.4

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

    if -7.562067749692457e+208 < z

    1. Initial program 1.7

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

    2. Simplified1.9

      \[\leadsto \color{blue}{z \cdot y + \left(a \cdot \left(t + z \cdot b\right) + x\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.562067749692457 \cdot 10^{+208}:\\ \;\;\;\;\left(b \cdot a + y\right) \cdot z + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot y + \left(\left(t + z \cdot b\right) \cdot a + x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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)))