Average Error: 1.9 → 0.7
Time: 15.2s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -4.474709576506922 \cdot 10^{+176}:\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \mathbf{elif}\;b \le 2.2669484073702458 \cdot 10^{-100}:\\ \;\;\;\;y \cdot z + \left(\left(t + z \cdot b\right) \cdot a + x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;b \le -4.474709576506922 \cdot 10^{+176}:\\
\;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\

\mathbf{elif}\;b \le 2.2669484073702458 \cdot 10^{-100}:\\
\;\;\;\;y \cdot z + \left(\left(t + z \cdot b\right) \cdot a + x\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r34504218 = x;
        double r34504219 = y;
        double r34504220 = z;
        double r34504221 = r34504219 * r34504220;
        double r34504222 = r34504218 + r34504221;
        double r34504223 = t;
        double r34504224 = a;
        double r34504225 = r34504223 * r34504224;
        double r34504226 = r34504222 + r34504225;
        double r34504227 = r34504224 * r34504220;
        double r34504228 = b;
        double r34504229 = r34504227 * r34504228;
        double r34504230 = r34504226 + r34504229;
        return r34504230;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r34504231 = b;
        double r34504232 = -4.474709576506922e+176;
        bool r34504233 = r34504231 <= r34504232;
        double r34504234 = a;
        double r34504235 = z;
        double r34504236 = r34504234 * r34504235;
        double r34504237 = r34504236 * r34504231;
        double r34504238 = x;
        double r34504239 = y;
        double r34504240 = r34504239 * r34504235;
        double r34504241 = r34504238 + r34504240;
        double r34504242 = t;
        double r34504243 = r34504234 * r34504242;
        double r34504244 = r34504241 + r34504243;
        double r34504245 = r34504237 + r34504244;
        double r34504246 = 2.2669484073702458e-100;
        bool r34504247 = r34504231 <= r34504246;
        double r34504248 = r34504235 * r34504231;
        double r34504249 = r34504242 + r34504248;
        double r34504250 = r34504249 * r34504234;
        double r34504251 = r34504250 + r34504238;
        double r34504252 = r34504240 + r34504251;
        double r34504253 = r34504247 ? r34504252 : r34504245;
        double r34504254 = r34504233 ? r34504245 : r34504253;
        return r34504254;
}

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

Original1.9
Target0.4
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -4.474709576506922e+176 or 2.2669484073702458e-100 < b

    1. Initial program 0.7

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

    if -4.474709576506922e+176 < b < 2.2669484073702458e-100

    1. Initial program 2.6

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

    2. Simplified0.7

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.474709576506922 \cdot 10^{+176}:\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \mathbf{elif}\;b \le 2.2669484073702458 \cdot 10^{-100}:\\ \;\;\;\;y \cdot z + \left(\left(t + z \cdot b\right) \cdot a + x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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)))