Average Error: 2.1 → 0.6
Time: 3.9s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.0890740179526285 \cdot 10^{-10} \lor \neg \left(b \le 1.3831953550132272 \cdot 10^{-189}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(a \cdot \left(z \cdot b\right)\right)}^{1}\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;b \le -1.0890740179526285 \cdot 10^{-10} \lor \neg \left(b \le 1.3831953550132272 \cdot 10^{-189}\right):\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(a \cdot \left(z \cdot b\right)\right)}^{1}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r712987 = x;
        double r712988 = y;
        double r712989 = z;
        double r712990 = r712988 * r712989;
        double r712991 = r712987 + r712990;
        double r712992 = t;
        double r712993 = a;
        double r712994 = r712992 * r712993;
        double r712995 = r712991 + r712994;
        double r712996 = r712993 * r712989;
        double r712997 = b;
        double r712998 = r712996 * r712997;
        double r712999 = r712995 + r712998;
        return r712999;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r713000 = b;
        double r713001 = -1.0890740179526285e-10;
        bool r713002 = r713000 <= r713001;
        double r713003 = 1.3831953550132272e-189;
        bool r713004 = r713000 <= r713003;
        double r713005 = !r713004;
        bool r713006 = r713002 || r713005;
        double r713007 = x;
        double r713008 = y;
        double r713009 = z;
        double r713010 = r713008 * r713009;
        double r713011 = r713007 + r713010;
        double r713012 = t;
        double r713013 = a;
        double r713014 = r713012 * r713013;
        double r713015 = r713011 + r713014;
        double r713016 = r713013 * r713009;
        double r713017 = r713016 * r713000;
        double r713018 = r713015 + r713017;
        double r713019 = r713009 * r713000;
        double r713020 = r713013 * r713019;
        double r713021 = 1.0;
        double r713022 = pow(r713020, r713021);
        double r713023 = r713015 + r713022;
        double r713024 = r713006 ? r713018 : r713023;
        return r713024;
}

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
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -1.0890740179526285e-10 or 1.3831953550132272e-189 < b

    1. Initial program 1.0

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

    if -1.0890740179526285e-10 < b < 1.3831953550132272e-189

    1. Initial program 3.8

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
    2. Using strategy rm

    3. Applied pow13.8

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot \color{blue}{{b}^{1}}\]

    4. Applied pow13.8

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot \color{blue}{{z}^{1}}\right) \cdot {b}^{1}\]

    5. Applied pow13.8

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\color{blue}{{a}^{1}} \cdot {z}^{1}\right) \cdot {b}^{1}\]

    6. Applied pow-prod-down3.8

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(a \cdot z\right)}^{1}} \cdot {b}^{1}\]

    7. Applied pow-prod-down3.8

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\left(a \cdot z\right) \cdot b\right)}^{1}}\]

    8. Simplified0.0

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\color{blue}{\left(a \cdot \left(z \cdot b\right)\right)}}^{1}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.0890740179526285 \cdot 10^{-10} \lor \neg \left(b \le 1.3831953550132272 \cdot 10^{-189}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(a \cdot \left(z \cdot b\right)\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(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)))