Average Error: 2.0 → 0.7
Time: 4.3s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b = -\infty \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 1.8357449125512327 \cdot 10^{262}\right):\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b = -\infty \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 1.8357449125512327 \cdot 10^{262}\right):\\
\;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r632180 = x;
        double r632181 = y;
        double r632182 = z;
        double r632183 = r632181 * r632182;
        double r632184 = r632180 + r632183;
        double r632185 = t;
        double r632186 = a;
        double r632187 = r632185 * r632186;
        double r632188 = r632184 + r632187;
        double r632189 = r632186 * r632182;
        double r632190 = b;
        double r632191 = r632189 * r632190;
        double r632192 = r632188 + r632191;
        return r632192;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r632193 = x;
        double r632194 = y;
        double r632195 = z;
        double r632196 = r632194 * r632195;
        double r632197 = r632193 + r632196;
        double r632198 = t;
        double r632199 = a;
        double r632200 = r632198 * r632199;
        double r632201 = r632197 + r632200;
        double r632202 = r632199 * r632195;
        double r632203 = b;
        double r632204 = r632202 * r632203;
        double r632205 = r632201 + r632204;
        double r632206 = -inf.0;
        bool r632207 = r632205 <= r632206;
        double r632208 = 1.8357449125512327e+262;
        bool r632209 = r632205 <= r632208;
        double r632210 = !r632209;
        bool r632211 = r632207 || r632210;
        double r632212 = r632195 * r632203;
        double r632213 = r632198 + r632212;
        double r632214 = r632199 * r632213;
        double r632215 = r632193 + r632214;
        double r632216 = r632196 + r632215;
        double r632217 = r632211 ? r632216 : r632205;
        return r632217;
}

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

Original2.0
Target0.3
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < -inf.0 or 1.8357449125512327e+262 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))

    1. Initial program 16.7

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

    2. Simplified3.8

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

    if -inf.0 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < 1.8357449125512327e+262

    1. Initial program 0.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b = -\infty \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 1.8357449125512327 \cdot 10^{262}\right):\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))