Average Error: 2.1 → 1.2
Time: 5.2s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 3.279955610243209304726884915279708655754 \cdot 10^{-35}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;a \le 3.279955610243209304726884915279708655754 \cdot 10^{-35}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r628018 = x;
        double r628019 = y;
        double r628020 = z;
        double r628021 = r628019 * r628020;
        double r628022 = r628018 + r628021;
        double r628023 = t;
        double r628024 = a;
        double r628025 = r628023 * r628024;
        double r628026 = r628022 + r628025;
        double r628027 = r628024 * r628020;
        double r628028 = b;
        double r628029 = r628027 * r628028;
        double r628030 = r628026 + r628029;
        return r628030;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r628031 = a;
        double r628032 = 3.2799556102432093e-35;
        bool r628033 = r628031 <= r628032;
        double r628034 = x;
        double r628035 = y;
        double r628036 = z;
        double r628037 = r628035 * r628036;
        double r628038 = r628034 + r628037;
        double r628039 = t;
        double r628040 = r628039 * r628031;
        double r628041 = r628038 + r628040;
        double r628042 = r628031 * r628036;
        double r628043 = b;
        double r628044 = r628042 * r628043;
        double r628045 = r628041 + r628044;
        double r628046 = r628036 * r628043;
        double r628047 = r628039 + r628046;
        double r628048 = r628031 * r628047;
        double r628049 = r628034 + r628048;
        double r628050 = r628037 + r628049;
        double r628051 = r628033 ? r628045 : r628050;
        return r628051;
}

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
Target0.3
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < 3.2799556102432093e-35

    1. Initial program 1.5

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

    if 3.2799556102432093e-35 < a

    1. Initial program 4.0

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

    2. Simplified0.2

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 3.279955610243209304726884915279708655754 \cdot 10^{-35}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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)))